If the radius of a sphere is doubled,its volu | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(A) The volume $V$ of a sphere with radius $r$ is given by the formula $V = \frac{4}{3} \pi r^3$.If the radius is doubled,the new radius $r' = 2r$.The

Vedclass · Accepted Answer

$8$

Vedclass · Answer

(A) The volume $V$ of a sphere with radius $r$ is given by the formula $V = \frac{4}{3} \pi r^3$.If the radius is doubled,the new radius $r' = 2r$.The new volume $V'$ is given by $V' = \frac{4}{3} \pi (r')^3$.Substituting $r' = 2r$ into the formula,we get $V' = \frac{4}{3} \pi (2r)^3 = \frac{4}{3} \pi (8r^3) = 8 	imes (\frac{4}{3} \pi r^3)$.Therefore,$V' = 8V$.Thus,the volume becomes $8$ times the original volume.

If the radius of a sphere is doubled,its volume becomes $\ldots \ldots \ldots \ldots$ times the original volume.

Similar Questions

Six wooden cubes of length $3 \, cm$ are arranged in a row touching each other face to face. Find the total surface area of the solid formed in this manner. (in $cm^2$)

The radii of a frustum of a cone are $6 \, cm$ and $4 \, cm$. If its height is $9 \, cm$,its volume is $\ldots \ldots \ldots \pi \, cm^3$.

How many cones with diameter $7\,cm$ and height $3\,cm$ can be produced by melting a metallic sphere with diameter $21\,cm$?

The volume of a cone is equal to:

The base of a cone with radius $6 \, cm$ and height $8 \, cm$ is hemispherical. Find the curved surface area and the volume of the solid. $(\pi = 3.14)$

Vedclass Test Series

Exam Paper Generator

Online Exam Module