Mensuration Questions

The length of the diagonal of a square is 14cm. What is the area of this square?

A cube has a surface area of 5400square units. Its volume would increase approximately _______ if the side is increased by 5units.

The diagonal of a square is 10
2

​
cm, find its perimeter.

The area of a square is 60.5cm
2
. Find the length of its diagonal (in cm).

A triangle has a base of $13.9\text{cm}$ and a height of $11.3\text{cm}$. What is the area of the triangle?

A cone of height $12\text{cm}$ and diameter $10\text{cm}$ is mounted on a hemisphere of the same diameter. What is the volume of the solid thus formed?

Find the measure of the central angle of the arc whose length is $22\text{cm}$ and the radius of the circle is $28\text{cm}$.

A hemispherical bowl is $88\text{cm}$ round the brim. Assuming it to be full, how many persons may be served from it in hemispherical glasses, $7\text{cm}$ in diameter at the top? (Where $\pi =\frac{22}{7}$)

The area of an equilateral triangle is $9\sqrt{3}{\text{cm}}^2$, find its perimeter.

If the semi-perimeter and area of a rectangular field whose length and breadth are 'x' and 'y' is 12cm and 28cm
2
, respectively, then find the value of x
4
+x
2
y
2
+y
4
.

Find the in-radius (in cm) of an equilateral triangle whose sides are 6cm each.

The circumference of a circle is 88cm, find its diameter?

The area of the rhombus (in cm
2
) having each side equal to 13cm and one of its diagonals equal to 24cm is:

The circumference of a circle is 88cm, find its area?

The volume of a cube is four times the volume of a cuboid. If the sides of the cuboid are $32\text{cm}$, $8\text{cm}$ and $4\text{cm}$, then find the ratio of the total surface area of the cube to that of the cuboid.

Find the total surface area of a cube whose volume is 64cm
3
.

Find the area (in cm
2
) of a semi-circle of radius 28cm.

If the lengths of the two parallel sides of a trapezium are $7\text{cm}$ and $9\text{cm}$ and its area is $80{\text{cm}}^2$. Find the distance between its parallel sides (in $\text{cm}$).

A circus tent is cylindrical to a height of $3\text{ m}$ and conical above it. If the radius of the base is $50\text{ m}$ and the slant height of the cone is $52\text{ m}$, then the total area of the canvas required to make it is:

Find the volume (in ${\text{cm}}^3$) of a cuboid of length, breadth, and height of $10.5\text{cm}$, $8\text{cm}$, and $9\text{cm}$ respectively.

The length, breadth and height of a cuboid are 10cm, 6cm and 4cm respectively. What is the total surface area?

A sector is cut from a circle of diameter $42\text{ cm}$. If the angle of the sector is $150^{\circ }$, then what is its area in ${\text{cm}}^2$? (Take $\pi =\frac{22}{7}$)

What is the length of the side of an equilateral triangle, if its area is 36
3

​
sq cm?

What is the total surface area of a cone whose radius is $\frac{r}{4}$ and slant height is $4l$?

Find the area of a minor sector of a circle whose circumference is $88\text{cm}$ and the length of its minor arc is $22\text{cm}$ (use $\pi =\frac{22}{7}$).

The largest sphere is carved out of a cube of side $7\text{ cm}$. What is the volume of the sphere in ${\text{cm}}^3$? (Take $\pi =\frac{22}{7}$)

When a cone is sliced by a plane parallel to its base, but not passing through its apex, what is the shape of the resulting cross-section?

The lateral surface area of a cone is 550cm². If the diameter of the cone is 14cm, then the height of the cone is:

The volume of a solid sphere is 4851 m
3
. What is the surface area of the sphere? (Take π=
7
22
​
)

The volume of a cube is 64cm
3
. The total surface area of the cube is:

If the volume of a cuboid is $440{\text{cm}}^3$ and the area of its base is $88{\text{cm}}^2$, then the height of the cuboid is ______.

Find the area of a right angle whose base is 15 cm and hypotenuse is 17 cm.

A cone of radius 3.5cm and height 12cm is completely filled with water. This water is emptied into an empty cylindrical vessel of radius 7cm. What will be the height of water in this vessel?

How many spherical balls each of $2\text{cm}$ radius can be made out of a solid metallic cube of edge $44\text{cm}$? (Take $\pi =\frac{22}{7}$)

Find the length of the arc whose central angle is 45
∘
and the radius of the circle is 28cm. (Take π=
7
22
​
)

A sphere of radius $9\text{cm}$ is moulded to form a cylinder of radius $3\text{cm}$. Find the height of the cylinder.

The volumes of two spheres are in the ratio of $512:3375$. The ratio of their surface areas is:

The perimeter of one face of a cube is 40 cm. Its volume will be:

The total surface area of a hemisphere is 166.32 sq cm, find its radius?

The area of a circle is 616 sq cm, find its circumference?

A cone is cut through a plane parallel to its base and then the cone that is formed on one side of that plane is moved. The new part that is left over on the other side of the plane is called_______________.

The total surface area of a cube is $294{\text{cm}}^2$. What is the length of its diagonal?

The ratio of the length and breadth of a rectangular garden is 14: 11 and its perimeter is 800 m. Its area is equal to the area of a circular field. What is the perimeter (in m) of the circular field? (Take π=
7
22
​
)

Find the total surface area of a hemisphere with a radius of $11\text{cm}$?

If the surface areas of two spheres are in the ratio of 4:25, then find the ratio of their volumes.

Six solid cubes, each of side $10\text{cm}$, are melted to form a rectangular solid of base area $30\text{cm}\times 5\text{cm}$. The lateral surface area (in ${\text{cm}}^2$) of the resulting solid is:

The length, breadth and height of a solid cuboidal box are in the ratio 7:5:3 and its total surface area is 11502cm
2
. Its breadth is:

The length of the largest possible rod that can be placed in a cubical room is $42\sqrt{3}\text{m}$. The surface area (in ${\text{m}}^2$) of the largest possible sphere that fit within the cubical room is: [Use $\pi =\frac{22}{7}$ ]

The radius of the base of a solid right circular cylinder is 10.5 cm and its volume is 5197.5 cm
3
. What is the total surface area (in cm
2
) of the cylinder? (Take π=
7
22
​
)

A cone with radius 7m is 6m high. Find the volume (in m
3
) of the cone. (Take π=
7
22
​
)

If diagonal of a cube is
108

​
 cm, then the volume (in cm
3
) of the cube is:

The length of a rectangular plot is thrice its breadth. The area of the plot is $768{\text{m}}^2$. Find the perimeter of the plot.

What is the difference between the total surface area and the curved surface area of a hemisphere when the radius is 6.3cm? (Take π=
7
22
​
)

If the side length of a square garden is $2,800\text{meters}$, how much fencing is needed to enclose it?

Find the surface area (in ${\text{cm}}^2$) of a sphere of diameter $7\text{cm}$.

If the cylinder height is 9cm and the base area is 25πcm
2
, then find the total surface area.

If a cylinder of radius 7cm and height 9cm is melted and constructed into a cone of the same radius, what will be the height of this cone?

A rectangular field has its length and breadth in the ratio of $8:7$ respectively. A man riding a bicycle completes one lap of this field along its perimeter at a speed of $28.8\text{km/hr}$ in $2.5\text{minutes}$. What is the area of the field?

The height of one cone is 3 times the height of another cone, while its radius is half of the radius of the other cone. If their total volume is 100unit
3
, then the difference in the volumes of the cones is _______ unit
3
.

A rectangle of length $14\text{ cm}$ and breadth $7\text{ cm}$ is rotated about its shorter side to form a cylinder. What is the volume (in ${\text{cm}}^3$) of the cylinder so generated? (Take $\pi =\frac{22}{7}$)

Find the in-radius (in cm) of an equilateral triangle whose sides are 6 cm each.

If the radius of a sphere is increased by 2cm, its surface area increases by 704cm
2
. What was the radius of the sphere before the increase? (Use π=
7
22
​
)

The total surface area of a cube is 181.5cm
2
. Find its side (in cm).

A circle has a radius of $92.8\text{cm}$. What is the circumference of the circle? (Use $\pi =3.14$)

The length of the diagonal of a rectangle is $26\text{cm}$ and that of one side is $10\text{cm}$. What is the area of this rectangle?

Find the area (in cm
2
) of a circle with a maximum radius that can be inscribed in a rectangle of length 18cm and breadth 12cm.

The perimeter of the rectangle is 280m and the difference between its two sides is 40m. Find the side of a square whose area is equal to the area of this rectangle.

The circumference of a circle exceeds its diameter by 30 cm. The area (in cm
2
) of the circle is: (Take π=
7
22
​
)

The lateral surface area of a hemisphere is $693{\text{cm}}^2$. Its radius will be ________. (Take $\pi =\frac{22}{7}$)

A hemisphere has 14cm diameter. Find its volume.

In a rhombus, one diagonal is $40\text{cm}$ and the other diagonal is $22\text{cm}$ longer than half the first diagonal. Find the length of each side of the rhombus.

How many balls of radius 10cm can be made by melting a bigger ball of diameter 80cm?

The area of a sector of a circle is 88cm
2
and the angle of the sector is 36
∘
. Find the radius (in cm) of the circle. [Use π=
7
22
​
.]

If a cylinder of radius 4cm and height 8cm is melted and constructed into a cone of the same radius, what will be the height of this cone?

The length and breadth of a painting are 15cm and 10cm respectively. A 1cm wide border is made around the painting. What is the area of the border?

The length of one side and the diagonal of a rectangle are 5cm and 13cm respectively. Find its area (in cm
2
).

The base of a parallelogram is twice its height. If the area of the parallelogram is $338{\text{cm}}^2$, then find its height (in $\text{cm}$).

Find the volume (in cm
3
) of a cuboid of length, breadth, and height of 8.5cm, 6cm, and 7cm respectively.

What is the perpendicular distance (in cm) between the parallel sides of a trapezium whose area is 108sq cm and the lengths of the parallel sides are 9cm and 36cm?

The circumference of a circle is $88\text{cm}$. Find its radius (in $\text{cm}$).

A copper sphere of diameter $12\text{cm}$ is drawn into a wire of diameter $4\text{mm}$. What is the length (in $\text{cm}$) of the wire? (Where $\pi =\frac{22}{7}$)

A box has length $11.1\text{cm}$, width $5.5\text{cm}$ and height $7.7\text{cm}$. Find its total surface area.

The radius of a cylinder is 7 feet. Find the total surface area of the cylinder if the height of the cylinder is 14 feet. (Use π=
7
22
​
)

The length of a wire (in m) of 0.5mm radius that can be drawn after melting a solid copper sphere of diameter 12cm is:

If the volume of spheres are 27: 8, then their ratio of surface areas is:

Melting a hemisphere of radius 7 cm, four small identical spheres are made. What is the radius of these spheres?

The diagonal of a rectangular field is $15\text{m}$ and its area is $108{\text{m}}^2$. What is the cost of fencing the field at $\text{₹}50.50$ per $\text{m}$?

What is the length of the arc of a circle whose radius is $35\text{cm}$ and whose arc subtends an angle of $72^{\circ }$ at the centre of the circle?

The volume of a right circular cylinder of base radius r is obtained by multiplying its curved surface area by:

A circle circumscribes a rectangle whose sides are in the ratio of $4:3$. If the area of the rectangle is $192{\text{ cm}}^2$, then the perimeter (in $\text{cm}$) of the circle is:

The volume of a right circular cone is $2464{\text{cm}}^3$. If the radius of its base is $14\text{cm}$, then its curved surface area (in ${\text{cm}}^2$) is: (Take $\pi =\frac{22}{7}$)

A sphere of radius $10\text{cm}$ is melted and made into a cone of height $10\text{cm}$. Find the diameter of the cone.

How many metres of cloth will be required to make a conical tent, the radius of whose base is $21\text{metres}$ and height is $28\text{metres}$, if the width of the cloth is $5\text{metres}$? (Where $\pi =\frac{22}{7}$)

Half the perimeter of a rectangular garden, whose length is 8cm more than its width, is 42cm. Find the area of the rectangular garden.

If the volume of a cube is given as 12167cm
3
, then the surface area of the cube will be:

If the diagonal of a cube is $8\sqrt{3}\text{ cm}$, then its total surface area is:

Area of the part of $120^{\circ }$ of a circle is $\frac{66}{7}{\text{ cm}}^2$ then diameter of the circle is ($\pi =22/7$):

A hemispherical bowl has a 21 cm radius. It is to be painted inside as well as outside. The cost of painting it at the rate of ₹0.05 per cm
2
and assuming that the thickness of the bowl is negligible, is: (Use π=
7
22
​
)

If the diagonal of a square is doubled, then the area of the square will be:

If each side of a square field is increased by $12\%$, then by what percentage has the area of the field increased?