Area and Volume Formulas: Geometry Math Test – PDF Download

Question 1: Circle measures (2 points)

A circle has a diameter of \(16\text{ in}\). Give exact answers in terms of \(\pi\).

1. (1 point) Find the circumference.
2. (1 point) Find the area.

Question 2: Rearranged sectors (2 points)

A circle of radius \(12\text{ cm}\) is cut into many thin sectors that are rearranged into a shape close to a parallelogram.

1. (1 point) Find the length of the base in terms of \(\pi\).
2. (1 point) Find the area of the shape and state which circle formula it confirms.

Question 3: Slanted cylinder (2 points)

The slanted cylinder and the right cylinder each have a base radius of \(3\text{ cm}\) and a perpendicular height of \(10\text{ cm}\).

1. (1 point) Find the exact volume of the slanted cylinder.
2. (1 point) Name the principle that justifies your answer and state what it says about the cross sections.

Question 4: Oil drum (2 points)

A cylindrical oil drum has a diameter of \(24\text{ in}\) and a height of \(36\text{ in}\).

1. (1 point) Find its volume in terms of \(\pi\).
2. (1 point) One gallon is \(231\text{ in}^{3}\). Find the capacity in gallons to the nearest tenth.

Question 5: Pyramid height (2 points)

A square pyramid has a base side of \(6\text{ m}\) and a volume of \(150\text{ m}^{3}\).

1. (1 point) Find the height of the pyramid.
2. (1 point) Find the volume of a prism with the same base and the same height.

Question 6: Pile of sand (2 points)

A cone-shaped pile of sand has a diameter of \(10\text{ ft}\) and a height of \(6\text{ ft}\).

1. (1 point) Find the volume to the nearest hundredth.
2. (1 point) Sand weighs \(100\) pounds per cubic foot. Find the weight of the pile in pounds.

Question 7: Volume of a sphere (2 points)

A sphere has a radius of \(9\text{ cm}\). Find its volume in terms of \(\pi\) and to the nearest hundredth.

Question 8: Hemisphere and cylinder (3 points)

A cylinder and a cone each have a radius of \(6\text{ cm}\) and a height of \(6\text{ cm}\).

1. (1 point) Find the exact volume of the cylinder.
2. (1 point) Find the exact volume of the cone.
3. (1 point) Subtract, then use the sphere formula to show that the result equals the volume of a hemisphere of radius \(6\text{ cm}\).

Question 9: Cone candles (3 points)

Priya pours wax from a full cylindrical mold into small cone-shaped molds. The cylinder has a radius of \(4\text{ cm}\) and a height of \(9\text{ cm}\). Each cone has a radius of \(3\text{ cm}\) and a height of \(6\text{ cm}\).

1. (1 point) Find the volume of the cylinder in terms of \(\pi\).
2. (1 point) Find the volume of one cone in terms of \(\pi\).
3. (1 point) How many cone candles can she fill?

⬇ Download the Geometry Area and Volume Formulas test (PDF, 89 KB)

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