The ratio of the radii of two spheres is 3:4. | vedclass

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

Question

(D) Let the radii of the two spheres be $r_1$ and $r_2$. Given that $r_1 : r_2 = 3 : 4$.The volume of a sphere is given by the formula $V = \frac{4}{3

Vedclass · Accepted Answer

$27:64$

Vedclass · Answer

(D) Let the radii of the two spheres be $r_1$ and $r_2$. Given that $r_1 : r_2 = 3 : 4$.The volume of a sphere is given by the formula $V = \frac{4}{3} \pi r^3$.Therefore,the ratio of the volumes of the two spheres is $\frac{V_1}{V_2} = \frac{\frac{4}{3} \pi r_1^3}{\frac{4}{3} \pi r_2^3} = \left( \frac{r_1}{r_2} \right)^3$.Substituting the given ratio,we get $\frac{V_1}{V_2} = \left( \frac{3}{4} \right)^3 = \frac{3^3}{4^3} = \frac{27}{64}$.Thus,the ratio of their volumes is $27:64$.

The ratio of the radii of two spheres is $3:4$. Then,the ratio of their volumes is $\ldots \ldots \ldots$

Similar Questions

The shape of a gilli,in the gilli-danda game (see figure),is a combination of

How many balls with diameter $1 \, cm$ can be produced by melting a metallic cylinder with radius $6 \, cm$ and height $4 \, cm$?

Three metallic solid cubes whose edges are $3 \, cm$,$4 \, cm$,and $5 \, cm$ are melted and formed into a single cube. Find the edge of the cube so formed (in $cm$).

The ratio of the diameters of two cylinders is $3:4$ and the ratio of their heights is $4:5$. Then,the ratio of their volumes is ..... .

$A$ metallic sphere with radius $42\, cm$ is melted to cast $8000$ identical balls. Find the radius of these balls (in $cm$).

Vedclass Test Series

Exam Paper Generator

Online Exam Module