Geometry: Triangular Prism Surface Area
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Questions and Answers

What is the total surface area of the triangular prism with base 14 cm, height 4 cm, and length 7 cm?

  • 168 cm²
  • 224 cm²
  • 196 cm²
  • 266 cm² (correct)

What formula is used to find the area of the triangular base of a prism?

  • 1/2 * Base * Height (correct)
  • Base * Height
  • Base + Height
  • Base * Height / 2

For a triangular prism with a base of 5 cm and a height of 4 cm, what is the area of one triangular face?

  • 12 cm²
  • 20 cm²
  • 10 cm² (correct)
  • 14 cm²

How is the total surface area of a prism calculated?

<p>Sum all the surface areas of the faces (D)</p> Signup and view all the answers

What is the area of the two triangular bases for a prism with a base of 6 cm and height of 16 cm?

<p>96 cm² (D)</p> Signup and view all the answers

What is the total surface area formula for a triangular prism?

<p>2 * area of base + lateral area (B)</p> Signup and view all the answers

In calculating the surface area of a triangular prism, which dimensions are crucial?

<p>Base, height, and length (B)</p> Signup and view all the answers

What is the surface area if the dimensions of a triangular prism are base: 3 m, height: 4 m, and length: 5 m?

<p>36 m² (D)</p> Signup and view all the answers

What is the primary characteristic of a prism?

<p>Its bases are congruent shapes. (A)</p> Signup and view all the answers

Which is true about the net of a square-based pyramid?

<p>The triangular faces can overlap when folded. (B)</p> Signup and view all the answers

Identify a shape that has six congruent triangles and a hexagonal base.

<p>Hexagonal pyramid (B)</p> Signup and view all the answers

What should be done if a given net does not represent a solid shape?

<p>Ensure all faces connect appropriately. (A)</p> Signup and view all the answers

Which combination of shapes describes two congruent squares and four congruent rectangles?

<p>Rectangular prism (A)</p> Signup and view all the answers

What is essential for a net to represent a cylinder?

<p>It should include circular bases and a rectangular face. (B)</p> Signup and view all the answers

Which of the following is NOT a characteristic of a pyramid?

<p>It can have multiple bases. (D)</p> Signup and view all the answers

To derive the circumference of a circle with a diameter of 12 cm, which formula is used?

<p>C = πd (C)</p> Signup and view all the answers

What is the formula for calculating the volume of a triangular prism?

<p>Area of base * Length (C)</p> Signup and view all the answers

If the base area of a triangular prism is 5 m² and the length is 12 m, what is its volume?

<p>60 m³ (A)</p> Signup and view all the answers

What is the area of a triangle with a base of 7 cm and a height of 4 cm?

<p>14 cm² (C)</p> Signup and view all the answers

For a prism with a base area of 14 cm² and a length of 20 cm, what would be the volume?

<p>280 cm³ (A)</p> Signup and view all the answers

How do you calculate the area of a triangular base given a base of 15 cm and a height of 20 cm?

<p>1/2 * 15 cm * 20 cm (B)</p> Signup and view all the answers

If a triangular prism has a volume of 27.8 cm³ and a length of 5 cm, what is the area of its base?

<p>5.56 cm² (C)</p> Signup and view all the answers

For a triangular prism with a base of 6 cm and a height of 10 cm and a depth of 9 cm, what is its volume?

<p>120 cm³ (D)</p> Signup and view all the answers

If a prism holds 1200 mL of water, what is its corresponding volume in cubic centimeters?

<p>1200 cm³ (C)</p> Signup and view all the answers

What is the total surface area of a cylinder with a radius of 6 cm and a height of 5 cm, rounded to the nearest square centimeter?

<p>415 cm² (B)</p> Signup and view all the answers

How do you calculate the area of the rectangle for a cylinder?

<p>2πrh (D)</p> Signup and view all the answers

If a cylinder has a diameter of 8 cm, what is its radius?

<p>4 cm (B)</p> Signup and view all the answers

What is the area of one base of a cylinder with a radius of 4 cm?

<p>$50.27 cm²$ (D)</p> Signup and view all the answers

What is the formula used to determine the total surface area of a closed cylinder?

<p>2πr² + 2πrh (D)</p> Signup and view all the answers

Which calculation is incorrect for a cylinder with a radius of 8 cm and height of 12 cm?

<p>Perimeter of the base: $16 cm$ (A)</p> Signup and view all the answers

What would be the total surface area of a cylinder with a diameter of 9 m and height of 6.8 m after computing all dimensions?

<p>189 m² (C)</p> Signup and view all the answers

In an open cylinder, how is the surface area calculated differently compared to a closed cylinder?

<p>Only lateral area is calculated. (C)</p> Signup and view all the answers

What is the radius of a cylinder with a diameter of 15 m?

<p>7.5 m (B)</p> Signup and view all the answers

What is the formula to calculate the area of the circular base of a cylinder?

<p>$πr^2$ (B)</p> Signup and view all the answers

How do you calculate the volume of a cylinder?

<p>Base area × height (D)</p> Signup and view all the answers

What is the circumference of a cylinder with a radius of 6 cm?

<p>$12π$ cm (B)</p> Signup and view all the answers

What is the surface area of the curved portion of a roller with a diameter of 1.8 m and height of 2.6 m?

<p>$4.56π$ m² (D)</p> Signup and view all the answers

If the total surface area of a cylinder is 377 cm² and its height is 10 cm, what would be its circumference?

<p>37.7 cm (A)</p> Signup and view all the answers

What is the formula for calculating the volume of a cylinder given the radius and height?

<p>$πr^2h$ (D)</p> Signup and view all the answers

For a cylinder with a base area of 423 cm² and height of 9 cm, what is the approximate volume?

<p>3507 cm³ (B)</p> Signup and view all the answers

Which of these options are correct? (Select all that apply)

<p>Option 3 (B), Option 2 (C)</p> Signup and view all the answers

Flashcards

Handshake Problem

The total number of lines that can be drawn connecting all points, representing handshakes, in a circle.

Circumference of a circle

The perimeter of a circle, calculated by the formula C = πd (where 'C' is the circumference, 'π' is pi, and 'd' is the diameter).

Area of a circle

The area enclosed within a circle, calculated by the formula A = πr² (where 'A' is the area, 'π' is pi, and 'r' is the radius).

Area of a shape

The space occupied by a two-dimensional shape, measured in square units (e.g., cm², m²).

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Volume of a shape

The space occupied by a three-dimensional shape, measured in cubic units (e.g., cm³, m³).

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Prism

A geometric solid with two parallel congruent polygonal bases and rectangular lateral faces, forming a prism shape.

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Pyramid

A geometric solid with a polygonal base and triangular lateral faces that meet at a point called the apex.

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Cube

A geometric solid with a rectangular base and four rectangular lateral faces that are perpendicular to the base.

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Surface Area of a Triangular Prism

The sum of the areas of all the faces of a triangular prism.

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Area of a Rectangle

The area of a rectangle is calculated by multiplying its length and width.

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Area of a Triangle

The area of a triangle is calculated by multiplying its base and height, then dividing by two.

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Net of a Prism

A net is a 2D representation of a 3D object, showing all the faces laid out flat.

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Calculating Total Surface Area of a Prism

The total surface area of a prism is the sum of the areas of all its faces.

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Surface Area and Net

The surface area of a prism is the same as the area of its unfolded net.

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Dimensions of a Prism

The length, width, and height of a prism are all important dimensions for calculating its surface area.

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Calculating Surface Area: Triangular Prism

To calculate the surface area of a triangular prism, find the area of each rectangular face and the two triangular bases, then add them together.

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Net of a solid shape

A diagram that can be unfolded to show all of the faces of a solid shape. It's like a blueprint for a 3D object.

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Diameter of a circle

The distance across a circle, passing through the center.

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Radius of a circle

The distance from the center of a circle to any point on its edge.

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Volume of a solid shape

The amount of space a three-dimensional shape occupies. It's measured in cubic units.

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Surface Area of a Cylinder

The total surface area of a cylinder is calculated by adding the area of its two circular bases to the area of its rectangular lateral surface.

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Total Surface Area of a Cylinder

The total surface area of a cylinder is the combined area of all its surfaces.

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Lateral Surface Area of a Cylinder

The lateral surface area of a cylinder is the area of the rectangular side that wraps around the circular bases.

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Lateral Surface Area Formula

To calculate the lateral surface area of a cylinder, multiply the circumference of the circular base by the height of the cylinder: 2πrh.

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Volume of a triangular prism

The volume of a triangular prism is calculated by multiplying the area of its triangular base by its length.

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Calculating the volume of a triangular prism

To find the volume of a triangular prism, multiply the area of its triangular base by its length.

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Finding the area of a triangular base

If you know the volume of a triangular prism and its length, you can calculate the area of its base by dividing the volume by the length.

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Volume formula for a triangular prism

The volume of a triangular prism is equal to the product of its base area and its length.

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Dimensions of a triangular prism

The three dimensions of a triangular prism are: Length, Width, and Height.

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Volume of any prism

You can find the volume of a triangular prism by multiplying the area of the base by the length. This is the same method used for other prisms, just use the triangle area instead of the base area.

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Base of a prism

The volume of a prism depends on the shape of its base and its length. For a rectangular prism, the base is a rectangle, while for a triangular prism the base is a triangle.

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Radius

The distance from the center of a circle to any point on its edge. It is half of the circle's diameter.

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Curved Surface Area of a Cylinder

The curved surface area of a cylinder is calculated by multiplying the circumference of the base by the height of the cylinder.

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Volume of a cylinder

The volume of a cylinder is calculated by multiplying the area of its base by its height.

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Circumference

Circumference is the distance around a circle. It is calculated by multiplying the diameter of the circle by π (pi).

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Area of a Circular Base

The area of a circular base of a cylinder is calculated by using the formula πr² (pi times radius squared).

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Study Notes

Module 4: Prisms and Cylinders

  • Students are asked to record the number of people in a circle and the number of handshakes.
  • A table is provided to document the results
  • A pattern should be described for the number of handshakes in relation to the number of people.
  • Students are given a word search puzzle with words related to shapes, volume, and geometry.
  • Includes terms such as angle, area, base, capacity, cube, decagon, four, hexagon, meter, prism, pyramid, rectangle, square, two.

Area of Two Dimensional Figures

  • Given shapes (triangles) with base (b) and height (h) values.
  • Formula to calculate the area of triangle is 1/2 × base × height, or A = ½bh.
  • Formula for the Area of a circle A = πr²

Circle Calculations

  • Calculations related to the area of circle.
  • Formula: Area = π × radius².
  • Calculations related to Circumference of a circle.
  • Formula: Circumference = π × diameter

Surface Area of Prisms and Cylinders, Volume of Prisms

  • Techniques for calculating the surface area and volume of prisms and cylinders are described
  • Includes examples of calculating the surface area of rectangular prisms and triangular prisms with different dimensions and related calculations.
  • Examples of volume calculations for rectangular and triangular prisms.

More on Surface Area and Volume

  • More practise problems for calculating the surface area and volume of prisms and cylinders.
  • Included are practise questions with multiple shapes and dimensions
  • Information for calculating surface and volumes of shapes are presented.

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Related Documents

Module 4: Prisms and Cylinders PDF

Description

Test your understanding of the surface area calculations for triangular prisms. This quiz covers essential formulas and concepts related to triangular bases and overall surface area. Perfect for students diving into geometry and prism properties.

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