A solid sphere and a solid hemisphere have th | vedclass

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

Question

(A) Let the radius of the solid sphere be $r_1$ and the radius of the solid hemisphere be $r_2$.Total Surface Area $(TSA)$ of a sphere $= 4 \pi r_1^2$

Vedclass · Accepted Answer

$3 \sqrt{3} : 4$

Vedclass · Answer

(A) Let the radius of the solid sphere be $r_1$ and the radius of the solid hemisphere be $r_2$.Total Surface Area $(TSA)$ of a sphere $= 4 \pi r_1^2$.Total Surface Area $(TSA)$ of a hemisphere $= 3 \pi r_2^2$.Given that their total surface areas are equal:$4 \pi r_1^2 = 3 \pi r_2^2$$\frac{r_1^2}{r_2^2} = \frac{3}{4}$$\frac{r_1}{r_2} = \frac{\sqrt{3}}{2}$.Now,the ratio of their volumes is:$\frac{V_{	ext{sphere}}}{V_{	ext{hemisphere}}} = \frac{\frac{4}{3} \pi r_1^3}{\frac{2}{3} \pi r_2^3} = 2 	imes \left(\frac{r_1}{r_2}ight)^3$.Substituting the ratio $\frac{r_1}{r_2} = \frac{\sqrt{3}}{2}$:Ratio $= 2 	imes \left(\frac{\sqrt{3}}{2}ight)^3 = 2 	imes \frac{3 \sqrt{3}}{8} = \frac{3 \sqrt{3}}{4}$.

$A$ solid sphere and a solid hemisphere have the same total surface area. The ratio of their volumes is

Similar Questions

$A$ solid cylinder having a radius of base as $7 \, cm$ and length as $20 \, cm$ is bisected along its height to get two identical cylinders. What will be the percentage increase in the total surface area?

The total number of spherical bullets,each of diameter $5$ decimetre,that can be made by utilizing the maximum of a rectangular block of lead with $11$ $m$ length,$10$ $m$ breadth and $5$ $m$ width is (assume that $\pi > 3$)

If the area of the base,height,and volume of a right prism are $(3 \sqrt{3} / 2) P^{2} \, \text{cm}^{2}$,$100 \sqrt{3} \, \text{cm}$,and $7200 \, \text{cm}^{3}$ respectively,then the value of $P$ is?

The total surface area of a hemisphere is $41.58 \text{ cm}^2$. Find its curved surface area (in $\text{cm}^2$).

The edges of a cuboid are in the ratio $1: 2: 3,$ and its surface area is $88 \, cm^2.$ The volume of the cuboid is ........ $cm^3$.

Vedclass Test Series

Exam Paper Generator

Online Exam Module