Question

Suppose the sphere below with radius rhas a volume equal to 45 units. Findаthe volume of the sphere with twice the radius.-21A. 90 units3O B. 360 units3C. 180 units3D. 450 units2

Answer 1

he have

when r

Volume=45

we are request to find the volume of the sphere with twice radius (2r)

we can find the volume with the following formula

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

replacing volume

`45=(4)/(3)\pi *r^3`

solving for r

`(45*3)/(4\pi)=r^3`
`\sqrt[3]{(135)/(4\pi)}=r`

now we find the volume for 2r

`2r=2\sqrt[3]{(135)/(4\pi)}`
`V=(4)/(3)\pi(2r)^3`
`V=(4)/(3)\pi(2\sqrt[3]{(135)/(4\pi)})^3`
`V=(4)/(3)\pi(8(135)/(4\pi))`
`V=(8*135)/(3)`
`V=180`

then the volume of a sphere twice a radius is 360 units^3