Bidyut Guha Thakurta and Amitava Mitra Solutions for Exercise 1: EXERCISE 3

From a metal made hemisphere of radius $2 \mathrm{cm}$, a maximum spherical part is cut off. Find the price in $₹$ of the remaining part of metal if the price of $1 \mathrm{cc}$ of metal is $₹7$.

(Round off the answer to next whole number)

The external diameter of the mouth of a hemispherical bowl made of $1 \mathrm{cm}$ thick copper sheet is $12 \mathrm{cm}$. What will be weight of the bowl if $1 \mathrm{cc}$ of copper weighs $9 \mathrm{g}$?

The sum of radius of two spheres is $10 \mathrm{cm}$. The sum of their volumes is $880 \mathrm{cc}$. Find the product of their radius (as mixed fraction) in $\mathrm{sq}.\mathrm{m}$. [Take $\mathrm{\pi }=\frac{22}{7}$]

The weight of a solid sphere of radius $6 \mathrm{cm}$ is $27 \mathrm{kg}$. What is the weight in $\mathrm{kg}$ of a hollow sphere made of same metal and $2 \mathrm{cm}$ thickness with external radius $8 \mathrm{cm}$?

Ratio of the whole surface area of a solid sphere and a solid hemisphere of same radius is _____.

Number of surfaces of a sphere is _____.

Volume of a solid hemisphere of radius $\frac{a}{2} \mathrm{cm}$ is $\frac{\mathrm{\pi }}{6}{a}^3 \mathrm{cu}.\mathrm{cm}$

Number of surfaces of a solid hemisphere is $1$.