A hollow sphere of internal and external diam | vedclass

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

Question

(B) The volume of a hollow sphere is given by $V = \frac{4}{3} \pi (R^3 - r^3)$,where $R$ is the external radius and $r$ is the internal radius.Given:

Vedclass · Accepted Answer

$14$

Vedclass · Answer

(B) The volume of a hollow sphere is given by $V = \frac{4}{3} \pi (R^3 - r^3)$,where $R$ is the external radius and $r$ is the internal radius.Given: External diameter $= 8\,cm \implies R = 4\,cm$. Internal diameter $= 4\,cm \implies r = 2\,cm$.Volume of the hollow sphere $= \frac{4}{3} \pi (4^3 - 2^3) = \frac{4}{3} \pi (64 - 8) = \frac{4}{3} \pi 	imes 56\,cm^3$.When the sphere is melted into a cone,the volume remains constant.Volume of cone $= \frac{1}{3} \pi r_{cone}^2 h$.Given: Base diameter of cone $= 8\,cm \implies r_{cone} = 4\,cm$.Equating the volumes: $\frac{1}{3} \pi (4)^2 h = \frac{4}{3} \pi 	imes 56$.$16h = 4 	imes 56$.$h = \frac{224}{16} = 14\,cm$.

$A$ hollow sphere of internal and external diameters $4\,cm$ and $8\,cm$ respectively is melted into a cone of base diameter $8\,cm$. The height of the cone is......$cm$.

Similar Questions

The ratio of the curved surface area and volume of a cylinder is $1:7$. The ratio of the total surface area and volume is $187:770$. What is the ratio of its base radius to its height?

$A$ solid cylinder has a total surface area of $462 \, cm^2$. Its curved surface area is $\frac{1}{3}$ of its total surface area. The volume of the cylinder is.......$cm^3$.

Find the diagonal of a cuboid whose dimensions are $12\, m$ by $10\, m$ by $8\, m$.

Water is flowing at the rate of $3 \, km/h$ through a circular pipe of $20 \, cm$ internal diameter into a circular cistern of diameter $10 \, m$ and depth $2 \, m$. In how much time will the cistern be filled?

$A$ $4\, cm$ 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?

Vedclass Test Series

Exam Paper Generator

Online Exam Module