Mensuration Questions

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.

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

The ratio of length and breadth of a rectangle is $21:20$ and its perimeter is $164\text{cm}$. What is the length of its diagonal (in cm)?

If the surface areas of two spheres are in the ratio of 9: 49, then the ratio of their volumes is:

Three solid iron cubes of edges 8 cm, 10 cm and 12 cm are melted together to make a new cube. It is observed that 496 cm³ of the melted material is lost due to improper handling. The area (in cm²) of the whole surface of the newly formed cube is:

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

How many cubes of length 50 cm can be accommodated in a container of 5 m in length, 2 m in width and 5 m in height?

The radius and height of a cylinder are in the ratio 7:13 and its volume is 6006 cm
3
. Its radius will be: (Use π=
7
22
​
)

The dimensions of a pond are 20m, 14m and 6m. Find the capacity of the pond.

Find the surface area of a ball of radius 21 mm. (Use π=
7
22
​
)

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.

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 $\pi =\frac{22}{7}$)

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 $\pi =\frac{22}{7}$).

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 perimeter of an isosceles right-angled triangle having an area of 200cm
2
is:

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:

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

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 length and breadth of a rectangle are $12\text{cm}$ and $5\text{cm}$ respectively. What must be the length of its diagonal (in $\text{cm}$)?

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 ($\pi =22/7$):

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

The ratio of the area of a circle and the maximum square inside it will:

It is proposed to build a single circular park equal in area to the sum of areas of two circular parks of diameters $16\text{m}$ and $12\text{m}$. The radius of the new park would be

An edge of a cube measures $r\text{cm}$. If the largest possible right circular cone is cut out of this cube, then the volume of the cone (in ${\text{cm}}^3$) is

A solid cylinder has a total surface area of $462\text{sq.cm}$. If its curved surface area is one-third of its total surface area, then the volume of the cylinder will be

A rectangular piece of paper $11\text{cm}\times 4\text{cm}$ is folded without overlapping to make a cylinder of height $4\text{cm}$, then the volume of the cylinder will be

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

A solid sphere has a surface area of 616cm
2
. This sphere is now cut into two hemispheres. What is the total surface area of one of the hemispheres?

What is the area of a triangle with a base of $8\text{meters}$ and a height of $16\text{meters}$?

What is the volume of a cube whose side is $2.7\text{m}$ long?

If the length of the diagonal of a cube is 16
3

​
cm, what is its lateral surface area (in sq cm)?

What is the area (in cm
2
) of a sector of a circle, with central angle 75
∘
, when the diameter of the circle is 9cm?

If each side of a rectangular field is increased by 32%, then by how much percent does the area of the field increase?

The volumes of two cubes are in the ratio of 8:27. If the volume of the larger cube is 513 cm
3
more than that of the smaller cube, find the length of each side of the smaller cube.

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_______________.

A cuboid with dimensions 20cm×12cm×10cm is cut into 8 identical pieces by 3 cuts. What will be the total surface area of all the pieces?

An article is of size 9cm×6cm×3cm. The number of such articles that can be packed in a box measuring 63cm×42cm×21cm is:

The length of a rectangular plot is increased by $60\%$. By how much percentage should its breadth be decreased so that the total area remains the same?

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.

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
.

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
​
.]

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

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?

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

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?

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:

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 $\pi =\frac{22}{7}$)

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 $\pi =\frac{22}{7}$)

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 $\text{m}$?

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 $\pi =\frac{22}{7}$)

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 $\pi =\frac{22}{7}$)

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

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

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

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

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

If diagonal of a cube is
108

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

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
​
)

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

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

If each edge of a cube is doubled, then the percentage increase in its total surface area is

The perimeter of a rhombus whose diagonals are 10cm and 24cm is

The ratio of the heights of two right circular cones is 25:64 and the ratio of their diameters is 4:5. The ratio of their volumes is

A right circular cylinder of maximum volume is cut from a solid cube of edge $14\text{cm}$. The total surface of the cylinder is

The perimeter of a rhombus whose diagonals are $10\text{cm}$ and $24\text{cm}$ is

The ratio of the heights of two right circular cones is $25:64$ and the ratio of their diameters is $4:5$. The ratio of their volumes is

A right circular cylinder of maximum volume is cut from a solid cube of edge 14cm. The total surface area of the cylinder is