Question

A ball has a diameter of 9 in. It consists of 2 parts. The inside is a spherical core with a diameter of 6 in. Surrounding the core is a layer of polyurethane.

What is the volume of the polyurethane?

Use 3.14 to approximate pi. Round to the nearest hundredth if necessary.

Enter your answer in the box.

? in³

Answer 1

the answer i got is 268.47

Answer 2

Answer: 268.47 cubic inches.

Explanation:

Given: Diameter of ball = 9 in.

⇒ Radius of ball R=
`(9)/(2)=4.5\ in.`

Diameter of spherical core = 6 in.

⇒ Radius of spherical core r=
`(6)/(2)=3\ in.`

Now, the volume of the polyurethane is given by :-

`\text{Volume of polyurethane=Volume of ball- Volume of spherical core}\\\\\Rightarrow\text{Volume of polyurethane}=(4)/(3)\pi R^3-(4)/(3)\pi r^3\\\\\Rightarrow\text{Volume of polyurethane}=(4)/(3)\pi(R^3-r^3)\\\\\Rightarrow\text{Volume of polyurethane}=(4)/(3)(3.14)((4.5)^3-3^3)\\\\\Rightarrow\text{Volume of polyurethane}=268.47\ in.^3`