Question

The area of the largest cross section of a sphere and the circumference of the sphere are in the ratio 4:1.

The radius of the sphere is ___cm. The circumference of the sphere is about ___cm. The area of the largest cross section is about____ cm. The volume of the sphere is about ___cm​

Answer 1

`(a)\ r = 8cm`

`(b\ Area = 200.96cm^2`

`(c)\ Volume = 2143.573cm^3`

Explanation:

The largest cross-section of a sphere is the center.

So, we have:

`A : C = 4 : 1`

Where

`A = \pi r^2`

`C =2\pi r`

Solving (a): The radius

`A : C = 4 : 1` implies that

`\pi r^2 : 2\pi r = 4 : 1`

Express as fraction

`(\pi r^2 )/( 2\pi r) = (4 )/( 1)`

`(\pi r^2 )/( 2\pi r) = 4`

Divide by
`\pi r`

`(r)/( 2) = 4`

Make r the subject

`r = 4 * 2`

`r = 8cm`

Solving (b): Area of the largest cross-section.

`Area = \pi r^2`

`Area = 3.14 *8^2`

`Area = 200.96cm^2`

Solving (b): Volume of the sphere

`Volume =(4)/(3)\pi r^3`

`Volume =(4)/(3) * 3.14 * 8^3`

`Volume = 2143.573cm^3`