Question

Type the correct answer in each box. Use and, if necessary, round your answers to the nearest hundredth.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 cm2. The volume of the sphere is about cm3.

Answer 1

We are given the ratio

A : C = 4 : 1

where

A=area = pi*r^2

`A=\pi r^2`

C=circumference = 2pi*r

`C=2\pi r`

then

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

express as afraction

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

thus

`(r)/(2)=4`
`r=2*4=8`

then the radius is r=8cm

B)Circumference

`C=2\pi r=2\pi8=16\pi`
`C=16*3.14=50.24`

the circumference is 50.2 cm

C)Area

`A=\pi r^2`
`A=3.14*8^2=200.96`

then the Area is 201.0 cm^2

D)Volume

`V=(4)/(3)\pi r^3`
`V=(4)/(3)*3.14*8^3`
`V=2143.573`

then the volume is

V=2143.6 cm^3