NCERT Solutions for Chapter: Surface Areas and Volumes, Exercise 1: Exercise

A metal memento has to be prepared by placing a solid sphere on a solid cylinder as shown in the figure. Find the quantity of metal required to prepare this memento, such that the radius of the cylinder is $6 \mathrm{cm}$ and its height is $14 \mathrm{cm}$ and the radius of the sphere is $2.1 \mathrm{cm}$. And also calculate the cost of painting the surface of the sphere with golden colour at the rate of $10$ paise per ${\mathrm{cm}}^2$.

The surface area of a solid spherical ball is $s {\mathrm{cm}}^2$. It is cut into $4$ identical pieces as shown below.

Find the total surface area of $4$ identical pieces of the solid spherical ball in term of $s$. Show your work.

Shown below is a small model of a cement mixer. The radius of the bottom of the drum is $5 \mathrm{cm}$ and that of the top of the drum is $2 \mathrm{cm}$.

Find the maximum quantity of cement, rounded to the nearest whole number, that the drum can hold. Show your steps. (Note: Take $\pi = \frac{22}{7}$)

A $5.54 \mathrm{l}$ watering can sprinkles water at the rate of $500 \mathrm{ml}/\min$, The can has a diameter of $14 \mathrm{cm}$ and is initially filled to its full capacity.

What is the height of water in the can after it is used for $8$ minutes? Show your work. (Note: Take $\pi = \frac{22}{7}$)

Two people have an equal amount of moulding clay. They make different solids of the same circular radius out of it- cylinder and hemisphere.

State true or false for the given statements and justify your answer.

1. Simran said, "The curved surface area of the cylinder is larger."
2. Manoj said, "Both the solids have the same curved surface area."

A bird feeder tube has a diameter of $8 \mathrm{cm}$ and height of $28 \mathrm{cm}$. The tube has $7$ circular openings of $2 \mathrm{cm}$ diameter each for the birds to eat from. The tube can hold a maximum of $3 \mathrm{kg}$ of bird food.

If the birds eat an average of $75 \mathrm{g}$ of food per hour, what will be the height of the food in the tube after $5$ hours? Show your work. (Note: Take $\pi = \frac{22}{7}$)

A semi-circular waffle sheet of radius $5 \mathrm{cm}$ is folded into an ice-cream cone as shown below.

Due to overlap while folding, the radius of the base of the cone is $80\%$ of what it would be without overlap. Find the approximate volume of the cone. Show your work. (Note: Take $\pi = \frac{22}{7}$)

Water is supplied to a village through a water tanker.

The water tanker is cylindrical in shape with diameter $110 cm$ and height $118 cm$. A total of $30,000$ litres of water is supplied through the tanker.

How many times was the water tanker used? (The tanker was always used at full capacity.) (Use $\pi =3.14$ and $1m^3=1000$ litres)