Tamil Nadu Board Solutions for Chapter: Mensuration, Exercise 15: Exercise 7.2

A cylindrical glass with diameter $20 \mathrm{cm}$ has water to a height of $9 \mathrm{cm}.$ A small cylindrical metal of radius $5 \mathrm{cm}$ and height $4 \mathrm{cm}$ is immersed in it completely. Calculate the raise of the water in the glass in $\mathrm{cm}$?

If the circumference of a conical wooden piece is $484 \mathrm{cm}$ then find its volume when its height is $105 \mathrm{cm}$.

A conical container is fully filled with petrol. The radius is $10 \mathrm{m}$ and the height is $15 \mathrm{m}$. If the container can release the petrol through its bottom at the rate of $25$ cu. meter per minute, in $k$ minutes the container will be emptied. Then find the value $k$. Round off your answer to the nearest minute.

A right-angled triangle whose sides are $6 \mathrm{cm}, 8 \mathrm{cm},$ and $10 \mathrm{cm}$ is revolved about the sides containing the right angle in two ways. The difference in volumes of the two solids so formed is $k {\mathrm{cm}}^3$. Find the value of $k$. (Consider $\mathrm{\pi }=\frac{22}{7}$ and write the answer as a fraction in its lowest form)

The volumes of two cones of same base radius are $3600 {\mathrm{cm}}^3$and $5040 {\mathrm{cm}}^3$. Find the ratio of heights in the same order. (Write the answer in the format $a:b$)

If the ratio of radii of two spheres is $4:7$, find the ratio of their volumes in the same order.

The outer and the inner surface areas of a spherical copper shell are $576\pi {\mathrm{cm}}^2$ and $324\pi {\mathrm{cm}}^2$ respectively. If the volume of the material required to make the shell is $V {\mathrm{cm}}^3$, then  the value of $V$ is $A\pi$. Find $A$.

A container open at the top is in the form of a frustum of a cone of height $16 \mathrm{cm}$ with radii of its lower and upper ends are $8 \mathrm{cm}$ and $20 \mathrm{cm}$ respectively. The cost of milk which can completely fill a container at the rate of $₹40$ per litre is $₹k$. Find the value of $k$. Take $\pi =\frac{22}{7}$ and write the answer in the lowest fraction.