Mensuration

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?

What is the maximum length of rod that can be placed inside a box having the shape of a cuboid of length $30 \mathrm{cm}$, breadth $24 \mathrm{cm}$ and height $18 \mathrm{cm}?$

The area of a rectangular room is $84 {\mathrm{m}}^2$. If the breadth of the room is $5 \mathrm{m}$ less than its length, the perimeter of the room (in meters) is ______.

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?

A certain amount is distributed among $\mathrm{A}, \mathrm{B} \mathrm{and} \mathrm{C}$ in the ratio of $3:5:7$ respectively. If $\mathrm{A}$ got $₹1196$ less than $\mathrm{C}$, what is the share of $\mathrm{B}?$

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 wheel of a motorbike makes $1000$ revolutions to cover a distance of $440 \mathrm{m}$. What is the diameter of the wheel (in $\mathrm{m}$)?

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?

$\mathrm{ABCD}$ is a square. $\mathrm{M}$ is the mid-point of $\mathrm{AB}$ and $\mathrm{N}$ is the mid-point of $\mathrm{BC}$. $\mathrm{DM}$ and $\mathrm{AN}$ are joined and they meet at $\mathrm{O}$. Then which of the following is not correct?

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 ______.

Read each of the following statements carefully and answer the questions.

In which of the following expressions will the expression P > S be definitely false?

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?

The product of two numbers is $4107$. If the H.C.F. of these numbers is $37$, then the greater number is:?