Geometry Unit Exam Part 2

1)

Find the volume of the cylinder. Keep your answer in terms of pi

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Explanation

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3) Find the volume of the following cone. Keep your answer in terms of pi

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Explanation

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4)

Find the Volume of the Sphere. Keep your answer in terms of pi

The volume of a sphere can be found using the formula V = (4/3)πr^3, where r is the radius of the sphere. This formula is derived from the fact that a sphere can be thought of as a collection of infinitely many infinitesimally thin circular disks stacked on top of each other. By integrating the area of these disks over the entire radius of the sphere, we can find the volume. The formula V = (4/3)πr^3 simplifies this process and allows us to directly calculate the volume using only the radius.

Explanation

The volume of a sphere can be found using the formula V = (4/3)πr^3, where r is the radius of the sphere. This formula is derived from the fact that a sphere can be thought of as a collection of infinitely many infinitesimally thin circular disks stacked on top of each other. By integrating the area of these disks over the entire radius of the sphere, we can find the volume. The formula V = (4/3)πr^3 simplifies this process and allows us to directly calculate the volume using only the radius.

5)

The cylinder above has a radius of

. The volume of the cylinder is

. What is the measurement of the height?

4 cm

8 cm

16 cm

32 cm

The volume of a cylinder is calculated by multiplying the area of the base (πr^2) by the height (h). In this case, the volume of the cylinder is given as 8 cm. Since the radius is not provided, we cannot directly calculate the height. Therefore, we cannot determine the measurement of the height based on the given information.

Explanation

The volume of a cylinder is calculated by multiplying the area of the base (πr^2) by the height (h). In this case, the volume of the cylinder is given as 8 cm. Since the radius is not provided, we cannot directly calculate the height. Therefore, we cannot determine the measurement of the height based on the given information.

6) Find the volume of the cone. Keep your answers in terms of pi.

The volume of a cone can be found using the formula V = (1/3)πr^2h, where r is the radius of the base and h is the height of the cone.

Explanation

The volume of a cone can be found using the formula V = (1/3)πr^2h, where r is the radius of the base and h is the height of the cone.