Question

suppse that you buy and exerice ball with diameter of 85 cm and your brother buys and exercise ball with 65 cm what is the diffrence bewtween the volume and surface are of both balls? round to the nearest 100

Answer 1

Given:

• Diameter of my ball = 85 cm

• Diameter of my brother's ball = 65 cm

Let's find the difference between the volume of the both balls and also let's find the difference between the surface area of both balls.

A ball has the shape of a sphere.

Therefore, we have the following formulas:

• Volume of a sphere formula:

`V=(\pi d^3)/(6)`

• Surface area of a sphere formula:

`A=\pi d^2`

Where d is the diameter.

• Now, to find the difference between the volume of both balls, we have:

`V_1=(\pi d^3)/(6)=(\pi85^3)/(6)=321555.09\approx321555\text{ cm}^3`

The volume of my ball is 321555 cubic cm.

`V_2=(\pi *65^3)/(6)=143793.3\approx143793\text{ cm}^3`

Volume of my brother's ball is 143793 cubic cm.

Therefore, to find the difference between the volume of both balls, we have:

V = V1 - V2 = 321555 - 143793 = 177762 cm³ = 177800 cm³

The difference between the volume of both balls is 177800 cm³

• Now for the surface area, we have:

`A_1=\pi d^2=\pi *85^2=22698.01=22698\text{ cm}^2`

The surface area of my ball is 22698 cm²

For surface area of my brother's ball:

`A_2=\pi d^2=\pi *65^2=13273.23\approx13273\text{ cm}^2`

The surface area of my brother's ball is 13273 cm².

Difference of surface areas:

A = A1 - A2 = 22698 - 13273 = 9425 cm² = 9400 cm²

Therefore, the difference between the surface area of both balls is 940O cm².

ANSWER:

• Difference between volume of both balls= 177800 cm³

• Difference between the surface area of both balls = 9400 cm²