Volumes of two spheres are in the ratio 64: 2 | vedclass

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

Question

(A) Let the radii of the two spheres be $r_1$ and $r_2$,respectively.The volume of a sphere is given by $V = \frac{4}{3} \pi r^3$.Given the ratio of v

Vedclass · Accepted Answer

$16:9$

Vedclass · Answer

(A) Let the radii of the two spheres be $r_1$ and $r_2$,respectively.The volume of a sphere is given by $V = \frac{4}{3} \pi r^3$.Given the ratio of volumes $V_1 : V_2 = 64 : 27$,we have:$\frac{\frac{4}{3} \pi r_1^3}{\frac{4}{3} \pi r_2^3} = \frac{64}{27}$$\frac{r_1^3}{r_2^3} = \frac{64}{27} = \left(\frac{4}{3}\right)^3$Taking the cube root on both sides,we get:$\frac{r_1}{r_2} = \frac{4}{3}$The surface area of a sphere is given by $A = 4 \pi r^2$.The ratio of their surface areas is:$\frac{A_1}{A_2} = \frac{4 \pi r_1^2}{4 \pi r_2^2} = \left(\frac{r_1}{r_2}\right)^2$Substituting the value of $\frac{r_1}{r_2}$:$\frac{A_1}{A_2} = \left(\frac{4}{3}\right)^2 = \frac{16}{9}$Thus,the ratio of their surface areas is $16:9$.

Volumes of two spheres are in the ratio $64: 27$. The ratio of their surface areas is

Similar Questions

$A$ cylindrical tank is closed at both the ends by hemispheres. Its radius is $2.1 \,m$ and the total height is $9.2 \,m$. How many litres of petrol can it contain?

The volume of a sphere with radius $1.5 \text{ cm}$ is $\ldots \ldots \ldots \text{ cm}^3$.

The volume of the largest right circular cone that can be cut out from a cube of edge $4.2 \,cm$ is (in $cm^3$)

The curved surface area of a cylinder is $132 \, cm^2$. If its height is $3 \, cm$,its diameter is $\dots \dots \dots \, cm$.

How many balls of radius $0.5\, cm$ can be produced by melting a metallic cylinder with radius $4\, cm$ and height $3\, cm$?

Vedclass Test Series

Exam Paper Generator

Online Exam Module