Surface area formulas: cubes, prisms, pyramids

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Questions and Answers

A prism has a base area of 25 square cm and a height of 8 cm. What is its volume?

  • 625 cubic cm
  • 33 cubic cm
  • 100 cubic cm
  • 200 cubic cm (correct)

If a rectangular prism has a length of 10 cm, a width of 5 cm, and a height of 4 cm, what is its volume?

  • 20 cubic cm
  • 200 square cm
  • 200 cubic cm (correct)
  • 19 cubic cm

A triangular prism has a base with an area of 30 square cm and a height of 6 cm. What is its volume?

  • 180 cubic cm
  • 60 cubic cm
  • 120 cubic cm
  • 90 cubic cm (correct)

What is the volume of a cube with sides measuring 4 cm?

<p>64 cubic cm (A)</p> Signup and view all the answers

A square pyramid has a base area of 36 square meters and a height of 9 meters. Determine the volume.

<p>108 cubic meters (C)</p> Signup and view all the answers

What is the volume of a cylinder with a radius of 5 cm and a height of 10 cm?

<p>250Ï€ cubic cm (C)</p> Signup and view all the answers

What is the volume of a cone with a radius of 3 cm and a height of 6 cm?

<p>18Ï€ cubic cm (A)</p> Signup and view all the answers

What is the volume of a sphere with a radius of 6 cm?

<p>288Ï€ cubic cm (D)</p> Signup and view all the answers

The surface area of a cube is 150 square cm. What is the length of each side?

<p>5 cm (A)</p> Signup and view all the answers

A rectangular prism has dimensions of length 8 cm, width 4 cm, and height 3 cm. What is its surface area?

<p>136 square cm (C)</p> Signup and view all the answers

Flashcards

Volume

The amount of space occupied by a three-dimensional figure.

Prism Volume

V = B x h, where B is the area of the base.

Rectangular Prism Volume

V = l x w x h, where l is length, w is width, and h is the height.

Triangular Prism Volume

V = 1/2 x a x b x h, where a and b are the base and height of the triangle, and h is the height of the prism.

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Cube Volume

V = s^3, where s is the side length.

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Pyramid Volume

V = 1/3 Bh, where B is the base area.

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Cylinder Volume

V = πr²h, where r is the radius and h is the height.

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Cone Volume

V = 1/3 πr²h, where r is the radius and h is the height.

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Sphere Volume

V = 4/3 πr³, where r is the radius.

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Surface area

Sum of all the areas that cover the surface of an object.

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Study Notes

  • Surface area is the sum of all the areas that cover the surface of an object.

Surface Area Formulae

  • Cube: Surface Area= 6s²
  • Rectangular Prism: Surface Area= 2lw + 2lh + 2wh
  • Square Pyramid: Surface Area= s² + 2sl
  • Cylinder: Surface Area= 2Ï€r² + 2Ï€rh
  • Cone: Surface Area= Ï€r² + Ï€rl
  • Sphere: Surface Area= 4Ï€r²

Example 1:

  • Finding the surface area of a cube with sides measuring 8 centimeters each.
  • Method: Using the formula for finding the surface area of a cube.
  • Surface Area = 6s²
  • Surface Area= 6(8 cm)²
  • Surface Area= 6(64 cm²)
  • Surface Area= 384 square centimeters or 384 cm²

Example 2:

  • Finding the surface area of the given square pyramid: SA = 384 square centimeters or 384 cm².

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