Embibe Experts Solutions for Chapter: Surface Areas and Volumes, Exercise 1: Uttarakhand Board-2018

Find the volume of cylinder having height $7 \mathrm{cm}$ and base diameter $10 \mathrm{cm}$.

A right circular cone is $8 \mathrm{cm}$ high and the radius of its base is $2 \mathrm{cm}$. The cone is melted and recast into the shape of a sphere. Find the diameter of the sphere.

The lower part of a tent of a circus is in the cylindrical shape and upper part is conical. If the diameter and the height of the cylindrical part are $126 \mathrm{m}$ and $5 \mathrm{m}$ respectively and the total height of the tent is $21 \mathrm{m}$, find the area of cloth used for making the tent. Also, find the cost of the cloth at the rent of $₹50$ per ${\mathrm{m}}^2$

A vessel is in the form of a hollow hemisphere mounted on a hollow cylinder. The diameter of the hemisphere is $14 \mathrm{cm}$ and the total height of the vessel is $13 \mathrm{cm}$. If the inner surface area of the vessel is $k {\mathrm{cm}}^2$, find $k$.

The radii of the ends of a frustum of a cone $45 \mathrm{cm}$ high are $28 \mathrm{cm}$ and $7 \mathrm{cm}$. Find its volume and the curved surface area. Take ($\mathrm{\pi }=\frac{22}{7}$)

A metallic sphere of radius $4.2 \mathrm{cm}$ is melted and recast into the shape of a cylinder of radius $6 \mathrm{cm}$. If the height of the cylinder is $k \mathrm{cm}$, find $k$.

A $20 \mathrm{m}$ deep well with diameter $7 \mathrm{m}$ is dug and the earth from digging is evenly spread out to form a platform $22 \mathrm{m}$ by $14 \mathrm{m}$. Find the height of the platform in $\mathrm{m}$