Question

Find the volume of the composite solid. Round your answer to the nearest tenth

Answer 1

V = 1206.3
`ft^(3)`

Explanation:

This shape is made up of a cylinder on the bottom and a cone on the top. We'll find the volumes of these shapes separately and then add them together.

Volume of a cylinder = area (of the base) x height

Substitute in the formula for the area of a circle.

V(cylinder) =
`\pi`
`r^(2)` x h

Substitute in the values for the radius (8) and height (4)

V(cylinder) =
`\pi` x
`8^(2)` x 4

Evaluate using a calculator

V(cylinder) = 804.2477

To the nearest tenth, V(cylinder) = 804.2

Volume of a cone =
`(\pi r^(2)h )/(3)`. This is the area of the circular part of the cone (
`\pi r^(2)`), multiplied by the height from the point to the base, all divided by 3.

Substitute in the values for the radius of the circle (8) and the height (6)

V(cone) =
`(\pi 8^(2) 6 )/(3)` (On the top it's
`\pi` x
`8^(2)` x 6)

Evaluate using a calculator

V(cone) = 402.1239

To the nearest tenth, V(cone) = 402.1

Total volume = V(cylinder) + V(cone)

= 804.2 + 402.1

= 1206.3
`ft^(3)`