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

$A$ metallic cone with radius $5 \, cm$ and height $8 \, cm$ is melted and recast to produce identical balls with diameter $0.5 \, cm$. Find the number of balls produced.

The radii of a frustum of a cone are $28 \, cm$ and $7 \, cm$ and its height is $72 \, cm$. Find its curved surface area,total surface area,and volume.

$1 \ m^{3} = \dots \dots \dots \text{ kilolitre}$

The volume of a sphere is $\ldots \ldots \ldots$

The radius and height of a cylinder are $1.4 \, cm$ and $10 \, cm$ respectively. Then,its curved surface area is $\ldots \ldots \ldots \, cm^2$.

Vedclass Test Series

Exam Paper Generator

Online Exam Module