Mensuration

The length of a rectangular plot is $20$metres more than its breadth. If the cost of fencing the plot @ Rs. $26.50$ per metre is Rs. $5300$, what is the length of the plot in metres?

An eccentric individual makes it his life's work to tie a rope around the earth's equator. He buys rope and makes an attempt. A rival of his, not to be outdone, decides to tie a rope around the earth's equator that is elevated from the ground by one metre at all points along the rope. How much more rope does he need? Assume the earth is perfectly spherical.

The radius of a circle is one-fourth of the length of a rectangle. The circumference of the circle is equal to the area of a square of $22 \mathrm{cm}$  side. If the perimeter of the rectangle is $668 \mathrm{cm}$, what is the breadth of the rectangle?

The sum of the circumference of a circle and the perimeter of a square is equal to $272$cm. The diameter of the circle is $56$cm. What is the sum of the areas of the circle and the square?

The cost of carpeting is $\mathrm{Rs}. 45 \mathrm{per} \mathrm{square} \mathrm{feet}$. What will be the cost of carpeting a circular floor with having a diameter of $19.6 \mathrm{feet}$? (Approx)

A circular park of $20 \mathrm{m}$ diameter has a circular path just inside the boundary of width $1 \mathrm{m}$. What is the area of the path?

From a rectangular metal sheet of sides $25 \mathrm{cm}$ and $20 \mathrm{cm}$, a circular sheet as large as possible is cut off. What is the area of the remaining sheet?

The length of a rectangular room is $17 \mathrm{m}$ and breadth is $4 \mathrm{m}$ less than length. What will be the total cost of carpeting this room if the cost of carpeting is $₹75$ per ${\mathrm{m}}^2?$

The length of a rectangular plot is decreased by $20$percent. By what percent the breadth is to be increased to maintain the same area?

The length of a rectangle is increased by $20$percent and its width is increased by fifty percent. By what percent does the area increase?

The perimeter of square is twice the perimeter of a rectangle. If the perimeter of the square is $56 \mathrm{cm}$ and the length of the rectangle is $9 \mathrm{cm}$. What is the difference between the breadth of the rectangle and the side of the square?

An eccentric individual makes it his life's work to tie a rope around the earth's equator. He buys rope and makes an attempt. A rival of his, not to be outdone, decides to tie a rope around the earth's equator that is elevated from the ground by one meter at all points along the rope. How much more rope does he need? Assume the earth is perfectly spherical.

A cusec of water is equivalent to _____

A rectangular garden is $100 \mathrm{m}\times 80 \mathrm{m}$. There is a path along the garden and just outside it. Width of the path is $10 \mathrm{m}$. The area of the path is ______.

The area of a square is three times the area of a rectangle. The length of the rectangle is $5$cms more than ${\left(5\right)}^2$ which is three times its breadth. What is the perimeter of the square?

The length of a rectangular plot is decreased by $20$percent. By what percent the breadth is to be increased to maintain the same area?

The height of a room is $\frac{1}{4}$ of the sum of length and breadth and the cost of painting its walls at the rate of $50 \mathrm{p}$ per ${\mathrm{m}}^2$  is $₹400$. Find its height?

A conical shaped container, whose radius of base is $r \mathrm{cm}$. and height is $h \mathrm{cm}$., is full of water. A sphere of radius $R$ is completely immersed in the container in such a way that the surface of sphere touches the base of the cone and its surfaces. The portion of water which comes out of the cone is_____.

If the volume of the cone is $616 {\mathrm{cm}}^3$ and the ratio of the side of the square to the radius of the cone is $2 : 1$. The perimeter of the square is $56 \mathrm{cm}$ and the height of the cylinder is equal to the height of the cone. If the volume of the cylinder is $7392 {\mathrm{cm}}^3$, find the radius of the cylinder.

The perimeter of the square is ------ $\mathrm{cm}$ and the area of the rectangle is $364 {\mathrm{cm}}^2$. The breadth of the rectangle is equal to the side of the square. If the height of the cylinder is $2 \mathrm{cm}$ less than the length of the rectangle and the breadth of the rectangle is double of the radius of the cylinder, then the curved surface area of the cylinder is ----- ${\mathrm{cm}}^2$.

a) $56, 1056$

b) $28, 1100$

c) $32, 1090$

d) $104, 988$