Mensuration

A right-angled triangle $ABC$ has sides $AB = 6$ cm and $BC = 8$ cm, with the right angle at $B$. Find the length of the hypotenuse $AC$ and the area of the triangle.

A rectangular field has length $30\text{ m}$ and breadth $20\text{ m}$. Find the cost of fencing it at Rs $10$ per meter.

What is the area of a right-angled triangle with sides $3\text{ cm}$, $4\text{ cm}$, and $5\text{ cm}$?

Find the area of a trapezium where the parallel sides are $10\text{ cm}$ and $14\text{ cm}$, and the distance between them is $5\text{ cm}$.

A path $5\text{ m}$ wide runs along the inside of a square park of side $100\text{ m}$. Find the area of the path.

The area of a triangle is equal to the area of a square whose side is $60\text{ m}$. Find the side of the triangle if its corresponding altitude is $90\text{ m}$.

The length of a rectangle is twice its breadth. If its area is $72\text{ cm}^2$, find its perimeter.

A rhombus has a perimeter of $52$ cm and one of its diagonals is $10$ cm. What is the area of the rhombus?

The perimeter of an isosceles triangle is $32$ cm. The ratio of the equal side to its base is $3:2$. Find the area of the triangle.

A path of uniform width $2$ m runs around the inside of a rectangular garden $30$ m long and $20$ m wide. Find the cost of leveling the path at Rs $12.50$ per $\text{m}^2$.

If the area of a circle is numerically equal to its circumference, find the radius of the circle.

Find the area of a quadrant of a circle whose circumference is $22$ cm.

The diameter of a wheel is $70$ cm. How many revolutions will it make to cover $110$ m?

If the area of a circle is $616$ cm$^2$, find its circumference.

The ratio of the circumferences of two circles is $3:4$. Find the ratio of their areas.

Find the area of the largest triangle that can be inscribed in a semi-circle of radius $r$.

A copper wire, when bent in the form of a square, encloses an area of $121$ cm$^2$. If the same wire is bent into the form of a circle, find the area of the circle.

Two circles touch externally. The sum of their areas is $130\pi\text{ cm}^2$ and the distance between their centers is $14\text{ cm}$. Find the radius of the larger circle.

A garden is in the shape of a rectangle $50\text{ m} \times 40\text{ m}$ with two semi-circles at the shorter ends. Find the cost of leveling the garden at Rs $10$ per square meter. (Use $\pi = 3.14$)

A copper wire is bent into the shape of an equilateral triangle and encloses an area of $121\sqrt{3}\text{ cm}^2$. If the same wire is bent into a circle, find the area of the circle. (Use $\pi = \frac{22}{7}$)

The area of the base of a right circular cylinder is $154\text{ cm}^2$ and its height is $15\text{ cm}$. Find its volume.

Find the capacity of a cylindrical vessel open at the top, whose internal diameter is $14\text{ cm}$ and height is $20\text{ cm}$. (Take $\pi = \frac{22}{7}$)

Find the surface area of a cube whose volume is $512\text{ cm}^3$.

The total surface area of a cylinder of base radius $r$ and height $h$ is given by:

How many liters of water can a cylindrical tank of radius $1\text{ m}$ and height $7\text{ m}$ hold? (Take $\pi = \frac{22}{7}$ and $1\text{ m}^3 = 1000$ liters)

The total surface area of a cuboid is $280\text{ cm}^2$. If its length and breadth are $10\text{ cm}$ and $8\text{ cm}$ respectively, find its height.

The diagonal of a cube is $12\sqrt{3}\text{ cm}$. Find its volume.

A well $14$ m deep is dug with a radius of $3$ m. The earth taken out is spread evenly all around it to a width of $7$ m to form an embankment. Find the height of the embankment.

A cuboid has a volume of $480$ cm$^3$. The area of its base is $80$ cm$^2$. If the length is $10$ cm, find the total surface area of the cuboid.

If the radius of a cylinder is doubled and the height is halved, what is the ratio between the new curved surface area and the original curved surface area?