M L Aggarwal Solutions for Chapter: Mensuration, Exercise 4: Exercise

Three cubes of silver with edges $3 \mathrm{cm}$, $4 \mathrm{cm} \mathrm{and} 5 \mathrm{cm}$ are melted and recast into a single cube. Find the cost of coating the surface of the new cube with gold at the rate of $₹3.50$ per square centimetre. 

The curved surface area of a hollow cylinder is $4375 {\mathrm{cm}}^2$, it is cut along its height and formed a rectangular sheet of width $35 \mathrm{cm}$. Let the perimeter of the rectangular sheet be $k \mathrm{cm}$. Find the value of $k$. 

A road roller has a diameter $0.7 \mathrm{m}$ and its width is $1.2 \mathrm{m}$. Find the least number of revolutions that the roller must take in order to level a playground of size $120 \mathrm{m} \times 44 \mathrm{m}$.

A company packages its milk powder in cylindrical container whose base has a diameter of $14 \mathrm{cm}$ and height $20 \mathrm{cm}$. Company places a label around the surface of the container (as shown in the figure). If the label is placed $2 \mathrm{cm}$ from top and bottom, let the area of the label be $k {\mathrm{cm}}^2$. Find the value of $k$.

The ratio between the curved surface and total surface of a cylinder is $1 : 2$. Let the volume of the cylinder be $k {\mathrm{cm}}^3$, given that its total surface area is $616 {\mathrm{cm}}^2$. Find the value of $k$.

The adjoining figure shows a metal pipe $77 \mathrm{cm}$ long. The inner diameter of cross section is $4 \mathrm{cm}$ and the outer one is $4.4 \mathrm{cm}$.

If its Inner curved surface area is $k {\mathrm{m}}^2$ then find $k$.

The adjoining figure shows a metal pipe $77 \mathrm{cm}$ long. The inner diameter of cross section is $4 \mathrm{cm}$ and the outer one is $4.4 \mathrm{cm}$.

If its outer curved surface area is $k {\mathrm{cm}}^2$ then find $k$.

The adjoining figure shows a metal pipe $77 \mathrm{cm}$ long. The inner diameter of cross-section is $4 \mathrm{cm}$ and the outer one is $4.4 \mathrm{cm}$. Let its total surface area be $k {\mathrm{cm}}^2$. Find the value of $k$.