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

Answer: 268.47 cubic inches.

Step-by-step explanation:

Given: Diameter of ball = 9 in.

⇒ Radius of ball R= $\frac{9}{2}=4.5\ in.$

Diameter of spherical core = 6 in.

⇒ Radius of spherical core r=  $\frac{6}{2}=3\ in.$

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

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

Answer 2

The answer i got is 268.47