Question

Carter is choosing clay for his pottery class. Clay is sold in three different-shaped solids at the craft store. The dimensions of each of these shapes is shown below.

Answer 1

`\boxed{\sf V_(cone) = 1017.36\ in \³}\\\boxed{\sf V_(cylinder) = 3052.08\ in\³}\\\boxed{\sf V_(sphere) = 3052.08\ in^3}`

Explanation:

`(1)/(3) \pi (9)^2 (12)\\324 * 3.14 \\ 1017.36`

`\pi (9)^2 (12)\\972 * 3.14\\ 3052.08`

`(4)/(3) \pi (9)^3\\972 * 3.14\\3052.08`

Answer 2

`\boxed{V_(cone) = 1017.36\ in.\³}`

`\boxed{V_(cylinder) = 3052.08\ in.\³}`

`\boxed{V_(sphere) = 3052.08\ in.^3}`

Explanation:

Volume of Cone:

`\sf V = (1)/(3) \pi r^2 h\\Where\ r = 9 , h = 12\\ V = (1)/(3) (3.14)(9)^2(12)\\V = (1)/(3) (3.14)(81)(12)\\V = (1)/(3) 3052.08\\`

V = 1017.36 in.³

Volume of Cylinder:

`\sf V = \pi r^3h\\V = (3.14)(9)^2(12)\\V = (3.14)(81)(12)`

V = 3052.08 in.³

Volume of Sphere:

`\sf V = (4)/(3) \pi r^3\\Where \ r = 9 \ in\\V = (4)/(3) (3.14)(9)^3\\V = (4)/(3) (3.14)(729)\\V = (9156.24)/(3)`

V = 3052.08 in.³