Subject Experts Solutions for Chapter: Mensuration, Exercise 1: TEST YOUR SKILLS

The parallel sides $\mathrm{AB}$ and $\mathrm{DC}$ of a trapezium $\mathrm{ABCD}$ are $51 \mathrm{cm}$ and $30 \mathrm{cm}$ respectively. If the other sides $\mathrm{AD}$ and $\mathrm{BC}$ are $20 \mathrm{cm}$ and $13 \mathrm{cm}$ respectively. Find the distance between the parallel sides and the area of the trapezium.

Two cubes of volume $512 {\mathrm{cm}}^3$ each are joined end to end. The surface area of the resulting cuboid is $k {\mathrm{cm}}^2$. Then find the value of $k$.

A well with $10 \mathrm{m}$ inside diameter is dug $8.4 \mathrm{m}$ deep. Earth taken out of it is spread all around it to a width of $7.5 \mathrm{m}$ to form an embankment. Find the height of embankment.

The total surface area of a cylinder is $462 {\mathrm{cm}}^2$. If it's curved surface area is one third of its total surface area, then the volume of the cylinder is $k {\mathrm{cm}}^3$. Find the value of $k$.

Top surface of a raised platform is in the shape of regular octagon as shown in the figure, if the area of the octagonal figure is $k {\mathrm{m}}^2$, find the value of $k$.

Verify the Euler's formula for the following polyhedron: Prism with equal base

Verify the Euler's formula for the following polyhedron:

Triangular pyramid

Verify the Euler's formula for the following polyhedron:

Rectangular pyramid