R S Aggarwal and Veena Aggarwal Solutions for Exercise 4: EXERCISE 15D

A hollow spherical shell is made of a metal of density $4.5 \mathrm{g} \mathrm{per} {\mathrm{cm}}^3$. If its internal and external radii are $8 \mathrm{cm}$ and $9 \mathrm{cm}$ respectively, find the weight of the shell.

A hemisphere of lead of radius $9 \mathrm{cm}$ is cast into a right circular cone of height $72 \mathrm{cm}$. Find the radius of the base of the cone. 

A hemispherical bowl of internal radius $9 \mathrm{cm}$ contains a liquid. This liquid is to be filled into cylindrical shaped small bottles of diameter $3 \mathrm{cm}$ and height $4 \mathrm{cm}$. How many bottles are required to empty the bowl? 

A hemispherical bowl is made of steel $0.5 \mathrm{cm}$ thick. The inside radius of the bowl is $4 \mathrm{cm}$. The volume of steel used in making the bowl is $k.83 {\mathrm{cm}}^3$

A hemispherical bowl is made of steel, $0.25 \mathrm{cm}$ thick. The inner radius of the bowl is $5 \mathrm{cm}$. If the outer curved surface area of the bowl is $k {\mathrm{cm}}^2$, then find the value of $k$. (Write the answer in decimal number)

A hemispherical bowl made of brass has inner diameter $10.5 \mathrm{cm}$. If the cost of tin-plating it on the inside at the rate of $₹32$ per $100 {\mathrm{cm}}^2$ is $₹k$, then find the value of $k$ (Correct up to two decimal places). $\left[\text{Take} \mathrm{\pi }=\frac{22}{7}\right]$

The diameter of the moon is approximately one fourth of the diameter of the earth. What fraction of the volume of the earth is the volume of the moon?

Volume and surface area of a solid hemisphere are numerically equal. What is the diameter of the hemisphere?