Brijesh Dwevedi and Jitendra Gupta Solutions for Chapter: Unit Tests (Mensuration) {Chapters Covered - 10, 11}, Exercise 3: UNIT TEST 3

The height of an equilateral triangle is $6 \mathrm{cm}$. Its area is

Each side of an equilateral triangle measures $8 \mathrm{cm}$. The area of the triangle is

Find the volume of the sphere whose radius is $5 \mathrm{m}$.

The height of a cone is $24 \mathrm{cm}$ and the diameter of its base is $14 \mathrm{cm}$. The curved surface area of the cone is

What will be the area of $∆ABC$, if the difference between the semi-perimeter's and the sides $a, b$ and $c$ of $∆ABC$ are $8 \mathrm{cm}, 7 \mathrm{cm}$ and $6 \mathrm{cm}$, respectively?

If every side of a triangle is doubled, then find the per cent increase in area of triangle so formed.

Calculate the area of the shaded region.

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 $396 {\mathrm{cm}}^2$.