Chhattisgarh Board Solutions for Exercise 7: Exercise – 3

Find the curved surface area in ${\mathrm{cm}}^2$ of the right circular cone in which slant height is $10 \mathrm{cm}$ and radius of the base is $7 \mathrm{cm}$. [Take $\pi =\frac{22}{7}$]

If the curved surface area of a cone $77\pi {\mathrm{cm}}^2$ and diameter of its base is $14 \mathrm{cm}$, then find the height of the cone.

Find the volume of a cone (in ${\mathrm{cm}}^3$) whose base area is $300 \mathrm{sq}.\mathrm{cm}$ and height is $15 \mathrm{cm}$.

Find the height of the cone (in $\mathrm{cm}$) if its volume is $550 {\mathrm{cm}}^3$ and its diameter is $10 \mathrm{cm}$.

The circumference of the base of a cone-shaped cup is $22 \mathrm{cm}$ and height is $6 \mathrm{cm}$. Then what is the maximum volume (in ${\mathrm{cm}}^3$) of water which can be kept in it.

If the radius of a $1 \mathrm{m}$ long metallic rod (in cylindrical shape) is $3.5 \mathrm{cm}$ then how many cones of radius $1 \mathrm{cm}$ and height $2.1 \mathrm{cm}$ can be formed by melting down the rod?

We have a right-angled triangle having sides $21 \mathrm{cm}, 28 \mathrm{cm}$ and $35 \mathrm{cm}$. If we take the side of $28 \mathrm{cm}$ as axis and rotate the triangle around it then write the name of the figure obtained and calculate its volume (in ${\mathrm{cm}}^3$).

If the radius of the base of a cone and a cylinder and their height is similar then calculate the ratio of their volumes.