Question

Find the approximate volume of the figure below, composed of a cone, a cylinder, and a hemisphere. If necessary, round your answer to the nearest tenth.

Answer 1

Answer:

Volume of the solid = 480.42m³

Step-by-step explanation:

To sov this question, we'll have to break the solid into different shapes of solid to solve it easily.

Volume of a cylinder = πr²h

volume of a hemisphere = 4/3πr³

Volume of a cone = ⅓πr²h

π = 3.14

r = 3m

h(cylinder) = 11m

Slant height of cone = 3√(2)

Height of cone = ?

To find height of cone, we can use pythagorean theorem

a² = b² + c²

[ 3√(2)]² = 3² + c²

9*2 = 9 + c²

C² = 18 - 9

C = 9m

Height of the cone = 9m

Volume of a cylinder = πr²h

V = 3.14 * 3² * 11

V = 310.86m³

Volume of the cylnder = 310.86m³

Volume of the hemisphere = 4/3πr³

V = 3.14 * 3³

V = 84.78m³

Volume of the hemisphere = 84.78m³

Volume of the cone = ⅓πr²h

V = ⅓ * 3.14 * 3² * 9

V = 84.78

Volume of the cone = 84.78m³

Volume of the solid = volume of cone + volume of hemisphere + volume of cylinder

Volume of the solid = 84.78 + 84.78 + 310.86

Volume = 480.42m³