Question

The figure is made up of a cylinder and a hemisphere. To the nearest whole number, what is the approximate volume of this figure? Use 3.14 to approximate π . Enter your answer in the box. in.³ A 7 inch cylinder with a dome on top of it that has a 5 inch diameter

Answer 1

I think it's 170 inches ³

Answer 2

Answer: The approximate volume of the composite figure made of a cylinder and a hemisphere is 170 in.³

Solution:

Volumen of the composite figure: V=?

V=Vc+Vh

1. Volume of the cylinder: Vc

Vc=∏r^2h

Radius of the cylinder: r

Height of the cylinder: h=7 in

Diameter of the cylinder: d=5 in

r=d/2

Replacing d by 5 in in the formula above:

r=(5 in)/2

r=2.5 in

Replacing ∏ by 3.14, r by 2.5 in, and h by 7 in, in the formula of Vc:

Vc=∏r^2h

Vc=3.14(2.5 in)^2(7 in)

Vc=3.14(6.25 in^2)(7 in)

Vc= 137.375 in³

2. Volume of the hemisphere: Vh

Vh=(4∏/6)r^3

Radius of the hemisphere = Radius of the cylinder: r=2.5 in

Replacing ∏ by 3.14, and r by 2.5 in, in the formula of Vh:

Vh=(4(3.14)/6)(2.5 in)^3

Vh=(2.093)(15.625 in³)

Vh=32.708 in³

Then the volume of the composite figure is:

V=Vc+Vh

Replacing Vc by 137.375 in³ and Vh by 32.708 in³ in the formula above:

V=137.375 in³ + 32.708 in³

V=170.083 in³

Rounding to the nearest whole number:

V=170 in³