Mensuration

If the area of a trapezium is $180\text{ cm}^2$ and its height is $9\text{ cm}$, find the sum of its parallel sides.

What is the area of a trapezium where parallel sides are $10\text{ cm}$ and $12\text{ cm}$ and height is $10\text{ cm}$?

A diagonal of a rhombus is $10\text{ cm}$ and its area is $60\text{ cm}^2$. What is the length of the other diagonal?

Find the area of a trapezium whose parallel sides are $7\text{ cm}$ and $9\text{ cm}$ and the height is $5\text{ cm}$.

A field is in the shape of a quadrilateral $ABCD$ as shown in the figure. The diagonal $AC$ is $24\text{ m}$ long. Two perpendiculars are dropped from the opposite vertices $B$ and $D$ onto the diagonal $AC$. The lengths of these perpendiculars $h_1$ and $h_2$ are $8\text{ m}$ and $13\text{ m}$ respectively. Find the total area of the field.

The area of a rhombus is $120\text{ cm}^2$ and one of the diagonals is $24\text{ cm}$. Find the side of the rhombus.

Find the area of a rhombus whose side is $6\text{ cm}$ and whose altitude is $4\text{ cm}$. If one of its diagonals is $8\text{ cm}$ long, find the length of the other diagonal.

A trapezium has an area of $210$ $\text{cm}^2$ and a height of $14$ cm. If one parallel side is $6$ cm longer than the other, find the length of the shorter parallel side.

In a quadrilateral $PQRS$, diagonal $PR = 20$ cm. If the area of triangle $PQR$ is $60$ $\text{cm}^2$ and the area of triangle $PSR$ is $80$ $\text{cm}^2$, find the sum of the perpendiculars from $Q$ and $S$ to $PR$.

Find the area of a trapezium whose parallel sides are $25$ cm and $13$ cm, and the non-parallel sides are $10$ cm each.

If the side of a square is doubled, by how many times does its area increase?

Find the area of a square whose diagonal is $4\sqrt{2}$ cm.

The area of a rectangle is $120\text{ cm}^2$. If its length is $15$ cm, find its breadth.

The perimeter of a square is $40$ cm. Find its area.

The parallel sides of a trapezium are in the ratio $3:4$ and the perpendicular distance between them is $12$ cm. If the area is $630\text{ cm}^2$, find the length of the shorter parallel side.

A square and a rectangle have the same perimeter. If the side of the square is $12$ cm and the length of the rectangle is $15$ cm, which figure has more area and by how much?

Find the area of the given polygon MNOPQR where MP = $9$ cm, and perpendiculars NA, OC, QB, RE are dropped on MP such that MA = $2$ cm, MC = $4$ cm, MB = $6$ cm, ME = $8$ cm and lengths of perpendiculars are NA = $3$ cm, OC = $2$ cm, QB = $4$ cm, RE = $1$ cm.

A swimming pool is in the shape of a large rectangle with two semi-circular ends. If the rectangular part is $20$ m long and $14$ m wide, find the total surface area of the water. (Use $\pi = 22/7$)

Find the area of a regular pentagon $ABCDE$ where each side is $12$ cm and the length of the perpendicular from the center to any side (apothem) is $8.25$ cm.

A garden path is designed using $5$ congruent rhombuses joined end-to-end. Each rhombus has diagonals of $6$ m and $4$ m. What is the total area of the path?

Find the side of a cube whose surface area is $600\text{ cm}^2$.

What is the total surface area of a hollow cylinder open at both ends if its radius is $r$ and height is $h$?

Find the height of a cuboid whose base area is $180\text{ cm}^2$ and volume is $900\text{ cm}^3$.

If the side of a cube is $3$ cm, find its lateral surface area.

If the radius of a cylinder is halved and its height is doubled, what happens to its curved surface area?

The lateral surface area of a hollow cylinder is $4224\text{ cm}^2$. It is cut along its height and formed a rectangular sheet of width $33$ cm. Find the perimeter of the rectangular sheet.

A suitcase with measures $80\text{ cm} \times 48\text{ cm} \times 24\text{ cm}$ is to be covered with a tarpaulin cloth. How many meters of tarpaulin of width $96$ cm is required to cover $100$ such suitcases?

A metal sheet of thickness $2$ cm is used to construct an open cylindrical water tank. The inner radius of the tank is $70$ cm and its inner height is $2$ m. The outside of the tank (curved surface and the base) needs to be painted with an anti-corrosive coating. What is the total area that needs to be painted? (Use $\pi = \frac{22}{7}$)

Three identical cubes of side $4$ cm are joined end-to-end to form a cuboid. Find the total surface area of the resulting cuboid.

A cuboid has total surface area $S$ and the sum of its edges is $E$. If the diagonal is $D$, which of the following relations is correct?

A right circular cylinder has a base radius of $7\text{ cm}$ and a height of $10\text{ cm}$. Find its volume. (Use $\pi = \frac{22}{7}$)

The side of a cube is $6\text{ cm}$. Calculate the volume of this cube.

A cuboidal box has dimensions $10\text{ cm} \times 8\text{ cm} \times 5\text{ cm}$. Find the volume of the box.

The volume of a cuboid is $440 \text{ cm}^3$ and the area of its base is $88 \text{ cm}^2$. Its height is:

What is the volume of a cylinder with base circumference $44$ cm and height $10$ cm? (Use $\pi = \frac{22}{7}$)

Two cylinders have same radii but their heights are in the ratio $2:3$. What is the ratio of their volumes?

A cube of side $4$ cm is painted on all sides and then cut into unit cubes ($1$ cm side). How many unit cubes will have no paint on them?

A cuboid of dimensions $60\text{ cm} \times 54\text{ cm} \times 30\text{ cm}$ is to be melted to form small cubes of side $6\text{ cm}$. How many such cubes can be formed?

If the side of a cube is doubled, how many times will its volume increase?

A hollow cylindrical pipe has an inner radius of $3\text{ cm}$ and an outer radius of $4\text{ cm}$. If the length of the pipe is $10\text{ cm}$, what is the volume of the material used to make the pipe? (Use $\pi = 22/7$)

What is the volume of a cuboid of dimensions $a \times a \times b$?

A container holds $5\text{ litres}$ of water. What is this volume in cubic centimeters?

Find the volume of a cylinder whose base diameter is $14\text{ cm}$ and height is $5\text{ cm}$. (Use $\pi = \frac{22}{7}$)

A rectangular box has volume $48\text{ m}^3$. If its length is $4\text{ m}$ and width is $3\text{ m}$, find its height.

A rectangular sheet of paper $44\text{ cm} \times 18\text{ cm}$ is rolled along its length to form a cylinder. Find the volume of the cylinder.

The capacity of a closed cylindrical vessel of height $1\text{ m}$ is $15.4\text{ litres}$. Find its radius. ($1000\text{ L} = 1\text{ m}^3$)

A cylinder of maximum volume is cut out from a solid wooden cube of side $14\text{ cm}$. Find the volume of the cylinder. (Use $\pi = \frac{22}{7}$)

An embankment is built around a circular well of diameter $7\text{ m}$ and depth $20\text{ m}$ by using the earth dug out from it. The embankment is in the shape of a hollow cylinder with an internal radius equal to the radius of the well and a width of $7\text{ m}$. Find the height of the embankment.

A solid metallic cuboid of dimensions $22\text{ cm} \times 15\text{ cm} \times 10\text{ cm}$ is melted and recast into a hollow cylindrical pipe. The internal radius of the pipe is $6\text{ cm}$ and its thickness is $1\text{ cm}$. Calculate the length of the pipe. (Take $\pi = \frac{22}{7}$)

A cylindrical water tank with a radius of $1.4\text{ m}$ is being filled at a constant rate of $22\text{ litres per second}$. A small outlet pipe at the bottom leaks water at a rate of $200\text{ cm}^3/\text{s}$. If the tank is initially empty, what will be the height of the water in the tank after exactly $5\text{ minutes}$? (Take $\pi = \frac{22}{7}$)