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?

The ratio of heights of two cylinders is $3:2$and the ratio of their radii is $6:7$. What is the ratio of their curved surface areas?

The side of a square is $40 \mathrm{cm}$. If its sides increased by $25\%$, what will be a percent increase in its area?

The ratio between the curved surface area and the total surface area of right circular cylinder is$1:2$ . If the total surface area is $616 {\mathrm{cm}}^2$, the volume of cylinder is _____.

A boat having a length $3\mathrm{m}$ and breadth $2\mathrm{m}$ is floating on a lake. The boat sinks by $1\mathrm{cm}$ when a man gets on it. The mass of the man is_____.

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 length, breadth and height of a cuboid are in the ratio $3 : 4 : 6$ and its volume is $576 {\mathrm{cm}}^3$. Find the whole surface area of the cuboid.

If the incentre of an equilateral triangle lies inside the triangle and its radius is $3 \mathrm{cm}$, then the side of the equilateral triangle is:

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?

A right circular cone is exactly fitted inside a cube in such a way that the edges of the base of the cone are touching the edges of one of the faces of the cube and the vertex touches the opposite face of the cube. If the volume of the cube is $343 {\mathrm{cm}}^3$. What is the approximate volume of the cone?

Two cones have their heights in the ratio $1 : 2$ and the diameters of their bases are in the ratio $2 : 1$. What will be the ratio of their volumes?

The perimeter of a square and a rectangle is$48$ m each. The differences between the areas of the two is $4$ m^$2$. The measurements of the rectangle (in metres) are

A right-angled isosceles triangle is inscribed in a semi-circle of radius $7 \mathrm{cm}$. The area enclosed by the semicircle but exterior to the triangle is:

Two small circular parks of diameters $16 \mathrm{m}, 12 \mathrm{m}$ are to be replaced by a bigger circular park. What would be the radius of this new park, if the new park occupies the same space as the two small parks?

If the base radius and the height of a right circular cone are increased $40\%$, then find the net $\%$ increase in volume _____.

The area of the triangle formed by the three lines $x=4$, $y=3$ and $3x+4y=12$ is equal to:

The perimeter of a circle, a square and an equilateral triangle are same, and their areas are C, S and T respectively. Which of the following statement is true?

If the volume and the surface area of a sphere are numerically equal, them the numerical value of then radius of the sphere is _____.

The area of a square is $441 {\mathrm{m}}^2$. It's side is equal to the radius of a circle. Find the circumference of the circle.

A playground is in the shape of a rectangle. A sum of $₹1000$ was spent to make the ground usable at the rate of$25 paise$ per square metre. The breadth of the ground is $50 metre$. If the length of the ground is increased by $20 metre$, what will be the expenditure in rupees at the same rate per square metre?