Question

Find the volume of the composite solid. Round your answer to the nearest hundredth. A composite shape consisting of a semi-cylinder placed atop a cube. The sides of the cube are labeled 4 inches. Find the volume of the composite solid. Round your answer to the nearest hundredth. A composite shape consisting of a semi-cylinder placed atop a cube. The sides of the cube are labeled 4 inches.

Answer 1

89.14 in.³

Explanation:

A semi-cylinder is half of a cylinder. A cube has equal sides. So if it is placed on top a cube, the following dimensions can be deduced:

The length of one side of the cube (s) = the diameter (d) of the semi-cylinder and also the height (h) of the semi-cylinder

Length of one side of the cube = 4 in.

Therefore,

Diameter of semi-cylinder = 4 in.

radius (r) = ½(4) = 2 in.

Height (h) of semi-cylinder = 4 in.

Let's find the volume of the composite solid

Volume of the composite solid = volume of semi-cylinder + volume of cube

= ½(π*r²*h) + (s³)

Volume of composite solid = ½(π*2²*4) + (4³)

= ½(50.27) + 64

= 89.135

≈ 89.14 in.³ (nearest hundredth)