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

$V=\frac{4}{3}\pi *r^3$

replacing volume

$45=\frac{4}{3}\pi *r^3$

solving for r

$\frac{45*3}{4\pi}=r^3$$\sqrt[3]{\frac{135}{4\pi}}=r$

now we find the volume for 2r

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

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