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

Volume of cuboid$=$Length$\times$Breadth$\times$Height.

If $V$ is the volume of cuboid whose length is $a$, breadth is $b$ and height is $c$ and $S$ is its total surface area, then prove that $\frac{1}{V}=\frac{2}{S}\left[\frac{1}{a}+\frac{1}{b}+\frac{1}{c}\right]$.

Two cubes each of $15 \mathrm{cm}$ sides are joined end to end. Find the total surface area of the resulting cuboid.

The radii of the ends of a frustum of a cone $45$cm high are $28$cm and $7$cm respectively, find the volume.

A hemispherical tank full of water is emptied by a pipe at the rate of $3\frac{4}{7}$ litters per second. How much time will it take to empty half the tank, if it is $3$m in diameter.(Take $\mathrm{\pi }=\frac{22}{7}$)

The formula of volume of cylinder is:

A cone of height $24 \mathrm{cm}$ and radius of base $6 \mathrm{cm}$ is made up of modelling clay. A child reshapes it in the form of a sphere. Find the radius of the sphere.

A medicine capsule is in the shape of a cylinder with two hemispheres stuck to each of its ends. The length of the entire capsule is $14 \mathrm{mm}$ and the diameter of the capsule is $5 \mathrm{mm}$. Find its surface area.