Podcast
Questions and Answers
A cylindrical tank has a radius of 3 meters and a height of 5 meters. Calculate its volume. Express your answer in terms of $\pi$.
A cylindrical tank has a radius of 3 meters and a height of 5 meters. Calculate its volume. Express your answer in terms of $\pi$.
$45\pi$ cubic meters
If the surface area of a square is $64 cm^2$, what is the length of one of its sides, and what is its perimeter?
If the surface area of a square is $64 cm^2$, what is the length of one of its sides, and what is its perimeter?
Side length = 8cm, Perimeter = 32cm
A rectangular garden is 10 meters long and 5 meters wide. How much fencing is needed to enclose the garden?
A rectangular garden is 10 meters long and 5 meters wide. How much fencing is needed to enclose the garden?
30 meters
A square prism has sides of length 4cm. What is the surface area of this prism?
A square prism has sides of length 4cm. What is the surface area of this prism?
A cone has a circular base with radius 6 and a perpendicular height of 8. Determine the volume of the cone. Express your answer in terms of $\pi$.
A cone has a circular base with radius 6 and a perpendicular height of 8. Determine the volume of the cone. Express your answer in terms of $\pi$.
The volume of a cube is 27 cubic meters. What is the length of each side?
The volume of a cube is 27 cubic meters. What is the length of each side?
Describe how the formula for the area of a rectangle is related to the formula for the area of a square.
Describe how the formula for the area of a rectangle is related to the formula for the area of a square.
Explain how to find the slant height of a square base pyramid.
Explain how to find the slant height of a square base pyramid.
A rectangular prism has dimensions length = 5, width = 3, and height = 4. What is its volume?
A rectangular prism has dimensions length = 5, width = 3, and height = 4. What is its volume?
If a circle's circumference is $10\pi$, what is its radius?
If a circle's circumference is $10\pi$, what is its radius?
Flashcards
Circle Formulas
Circle Formulas
Area: ( A = \pi r^2 ). Circumference: ( C = 2 \pi r )
Square Prism (Cube)
Square Prism (Cube)
A prism with square faces where length equals height. Volume: (V = a^3); Surface area: (6a^2).
Square Formulas
Square Formulas
Area (A = a^2 ) (length (\times) length). Perimeter (= 4a).
Rectangular Prism Formulas
Rectangular Prism Formulas
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Square Base Pyramid Formulas
Square Base Pyramid Formulas
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Slant Height
Slant Height
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Rectangle Formulas
Rectangle Formulas
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Right Cylinder Formulas
Right Cylinder Formulas
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Study Notes
- Study notes on geometric shapes.
Circle
- Area (A) = πr²
- Circumference = 2πr
Square
- Area = length × length = a²
- Perimeter = 4a
Rectangle
- Area (A) = length × breadth
- A = ab
- Perimeter = 2a + 2b
Right Cylinders
- Volume (V) = πr²h
- Surface area = 2πr² + 2πrh
Square Prism
- Note: length = breadth = height = a
- Volume (V) = a × a × a = a³
- Surface area = 6a²
Rectangular Prism
- Volume (V) = l × b × h
- Surface area = 2lb + 2lh + 2bh
Cones
- Volume (V) = (1/3)πr²H
- Surface area = πr² + (1/2)(2πr × h) = πr² + πrh
Square Base Pyramid
- Volume (V) = (1/3)a² × H
- Surface area = area of square + 4 × area of triangle
- Surface area = a² + 4(1/2 a⋅h)
- Surface area = a² + 2ah
- The slant height runs from the middle of the edge of the base to the apex
- Slant heights can be calculate using the perpendicular height and the dimensions of the base by using the Theorem of Pythagoras.
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