Subject Experts Solutions for Chapter: Mensuration, Exercise 5: SUMMATIVE ASSESSMENT

In the given figure, a square garden measuring $8 \mathrm{m}$ on a side is surrounded by a $1 \mathrm{m}$ wide path. If the area of the path is $k {\mathrm{m}}^2$, then find the value of $k$.

If the surface area of the given model is $k {\mathrm{cm}}^2$, then find the value of $k$.

If the area to be painted in the following block with a cylindrical hole is $k {\mathrm{cm}}^2$ then find $k$. Given that length is $15 \mathrm{cm}$, width is $12 \mathrm{cm}$, height is $20 \mathrm{cm}$ and radius of the hole is $2.8 \mathrm{cm}$. Take $\mathrm{\pi }=\frac{22}{7}$ and write answer up-to two decimal places.

Area of $4$ walls of a room is $108 {\mathrm{m}}^2$. If height and length of room is in ratio of $2:5$ and height and breadth in ratio $4:5$, and the area of floor of the room is $k {\mathrm{m}}^2$, find $k$.

How many bricks of size ($22\times 10\times 7$) ${\mathrm{cm}}^3$ are required to construct a wall $11 \mathrm{m}$ long, $3.5 \mathrm{m}$ high and $40 \mathrm{cm}$ thick, if the cement and sand used in the construction occupy $\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$10$}\right.$ th part of the wall?

A water tank built by municipality of a town to supply water to its $25000$ inhabitants at $125 \mathrm{l}$per day per person is $40 \mathrm{m}$ long and $31.25 \mathrm{m}$ broad. The tank, when it is full, can supply water for two days to the inhabitants of the town. Find the depth of the tank. What values of the municipality are being reflected here?

A $14 \mathrm{m}$ wide athletic track consists of two straight sections each $120 \mathrm{m}$ long joined by semi-circular ends with inner radius is $35 \mathrm{m}$. Calculate the area of the track in ${\mathrm{m}}^2$ and write only magnitude.

An open rectangular cistern when measured outside is $1.35 \mathrm{m}$ long, $1.08 \mathrm{m}$ broad and $90 \mathrm{cm}$ deep and is made of iron which is $2.5 \mathrm{cm}$ thick. Find the capacity of the cistern and the volume of the iron used.