The radii of two solid iron spheres are 1 , c | vedclass

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

Question

(D) The volume of a sphere is given by $V = \frac{4}{3} \pi r^3$.Total volume of the two solid spheres $= \frac{4}{3} \pi (1^3 + 6^3) = \frac{4}{3} \p

Vedclass · Accepted Answer

$1$

Vedclass · Answer

(D) The volume of a sphere is given by $V = \frac{4}{3} \pi r^3$.Total volume of the two solid spheres $= \frac{4}{3} \pi (1^3 + 6^3) = \frac{4}{3} \pi (1 + 216) = \frac{4}{3} \pi (217) \, cm^3$.Let the internal radius of the hollow sphere be $r \, cm$. The volume of the material of the hollow sphere is given by $V = \frac{4}{3} \pi (R^3 - r^3)$,where $R = 9 \, cm$ is the external radius.Equating the volumes: $\frac{4}{3} \pi (217) = \frac{4}{3} \pi (9^3 - r^3)$.$217 = 729 - r^3$.$r^3 = 729 - 217 = 512$.$r = \sqrt[3]{512} = 8 \, cm$.Thickness of the hollow sphere $=$ External radius $-$ Internal radius $= 9 \, cm - 8 \, cm = 1 \, cm$.

The radii of two solid iron spheres are $1 \, cm$ and $6 \, cm$ respectively. $A$ hollow sphere is made by melting the two spheres. If the external radius of the hollow sphere is $9 \, cm$,then its thickness (in $cm$) is

Similar Questions

The volume of the largest right circular cone that can be cut out of a cube of edge $7 \, cm$ is.....$cm^3$

$A$ $4\, cm$ cube is cut into $1\, cm$ cubes. What is the ratio of the total surface area of all the small cubes to the surface area of the large cube?

The weight of a solid cube of iron of $1 \, cm$ edge is $17 \, gm$. What should be the weight of a similar cube of edge $3 \, cm$? (in $gm$)

The diameter and slant height of a conical tomb are $28\, m$ and $50\, m$,respectively. The cost of whitewashing its curved surface at the rate of $80$ paise per $m^2$ is (in $Rs.$):

The radius of a wheel is $21 \, cm$. What is the distance (in $cm$) travelled by the wheel in $10$ revolutions?

Vedclass Test Series

Exam Paper Generator

Online Exam Module