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

This is the picture of an ice-cream cone.

The radius of the cone is $4 \mathrm{cm}$ and the height is $15 \mathrm{cm}$.

An ice-cream seller keeps $1/4^{\mathrm{th}}$ of its empty.

What is the volume $(\mathrm{in} \mathrm{cm}³)$ of the empty part of the cone?

A semi-circular sheet of metal of diameter $28 \mathrm{cm}$ is bent into an open conical cup. Then, the capacity of the cup is

A team of $10$ interns and $1$ professor from zoological department visited a forest, where they set up a conical tent for their accommodation. There they perform activities like planting saplings, yoga, cleaning lakes, testing the water for contaminants and pollutant levels and desilt the lake bed and also using the silt to strengthen bunds. Find the radius and height of the tent if the base area of tent is $154 {\mathrm{cm}}^2$ and curve surface area of the tent is $396 {\mathrm{cm}}^2$.

A solid cylinder of silver $9 \mathrm{cm}$ high and $4 \mathrm{cm}$ in diameter is melted and recast into a right circular cone of diameter $6 \mathrm{cm}$. Find the height and the total surface area of the cone. Give your answer correct to one decimal place. Take $\pi =3.14$.

Find the volume of the largest right circular cone that can be fitted in cube whose edge is $2 \mathrm{a}$ units.

A semicircular sheet of metal of diameter $28 \mathrm{cm}$ is bent into a form of open conical cup. The capacity of the cup$=$_____ ${\mathrm{cm}}^3$. (upto two decimal place)

The circumference of the base of $16 \mathrm{m}$ high solid cone is $33 \mathrm{m}$. Find the total surface area of the cone. (take, $\mathrm{\pi }=22/7$)

If the base diameter and the height of a cone are $10 cm$ and $12 cm$ respectively, then the slant height of the cone is _____.