Introduction to Mensuration

Q.

Question 65

The walls and ceiling of a room are to be plastered. The length, breadth and height of the room are 4.5 m, 3 m and 350 cm respectively. Find the cost of plastering at the rate of Rs. 8 per $m^2$.

Q.

If the radius of a circle is 14 cm then its circumference is:

1. 44 cm

2. 88 cm

3. 66 cm

4. 22 cm

Q.

What is the area of a circle with radius r?

1. $\pi r^2$ sq. units

2. $2\pi r^2$ sq. units

3. $4\pi r^2$ sq. units

4. $6\pi r^2$ sq. units

Q. If area of a square plate is 100 m², then what is the side length of the square plate and its perimeter respectively?

1. 10 m, 20 m

2. 10 m, 30 m

3. 5 m, 40 m

4. 10 m, 40 m

Q.

A parallelogram is called a Rectangle if two adjacent sides are equal.

1. True

2. False

Q.

Question 69

The areas of two circles are in the ratio 49 : 64. Find the ratio of their circumferences.

Q.

A larger wheel of diameter $50\mathrm{cm}$ is attached to a smaller wheel of diameter $30\mathrm{cm}$. Find the number of revolutions made by the smaller wheel, when the larger one makes $15$ revolutions.

Q.

Assertion: Area of an equilateral triangle of side ‘a’ is $=\frac{\sqrt{3}}{4}{a}^2$

Reason: The height of an equilateral triangle of side ‘a’ is $=\frac{\sqrt{3}}{4}{a}^2$

Which of the following is correct?

1. A is true and R is false.

2. A is false and R is true.

3. Both A and R are true and R is the correct explanation of A.

4. Both A and R are true but R is not the correct explanation of A.

Q.

A wire is bent to form a square of side $22\mathrm{cm}$. If the wire is rebent to form a circle, its radius is

1. $22\mathrm{cm}$

2. $14\mathrm{cm}$

3. $11\mathrm{cm}$

4. $7\mathrm{cm}$

Q.

There are two concentric circular tracks of radii $100\mathrm{m}$ and $102\mathrm{m}$ respectively. A runs on the inner track and goes once round the track in $1$ minute $30$ seconds while B runs on outer track in $1$ minute $32$ seconds. Who runs faster ?

Q.

Perimeter of a regular polygon = length of one side $\times$ ___________.

Q. _{a wheel has a diameter of 28 cm.find the distance covered by the wheel in 20 revolutions.}

Q.

The hour hand of a clock is 6.3 cm long. Find the distance covered by it in 2 days.

Q.

The perimeter of a square, whose each side is 11 cm, is same as the circumference of a circle. Find the area of the circle.

1. 90 cm²

2. 154 cm²

3. 164 cm²

4. 44 cm²

Q.

Find area of the parallelogram of base 10 cm & altitude 5 cm as shown in the figure.

1. $100c{m}^2$

2. $45c{m}^2$

3. $25c{m}^2$

4. $50c{m}^2$

Q.

The perimeter of rectangle is 80 metres and its length is 1 metre more than twice the breath what are it's length and bredth?

Q.

There is a rectangular park whose length is 20 m and width is 10 m. What is the length of fence surrounding it?

1. 20 m

2. 30 m

3. 40 m

4. 60 m

Q.

Question 72

Find the perimeter of the given figure.

Q. If the perimeter of a square field is 400 m, what is the length of each side of the field?

1. $150m$
2. $200m$
3. $100m$
4. $50m$

Q.

Find the circumference of the circle, whose area is 144 cm².

1. 12π cm

2. 46π cm

3. 72π cm

4. 24π cm

Q. The shape of a garden is rectangular in the middle and semi circular at the ends as shown in the diagram. The perimeter of this garden is

1. 62 m
2. 60 m
3. 45 m
4. 48 m

Q.

The circumference of a circle of diameter 10 cm is:

1. 31.4 cm

2. 3.14 cm

3. 0.314 cm

4. 314 cm

Q.

The perimeter of the above-shown figure is 9.5 cm.

1. True

2. False

Q.

Ram says that 22 bags of cement were required to cement a circular platform. If one bag of cement is required to cement an area of 7 m², then find the area and the radius of the circular platform.

1. 154 m², 7 m

2. 154 , 7 m

3. 154 m², 70 cm

4. 22 m², 7 m

Q. Question 3

36 unit squares are joined to form a rectangle with the least perimeter. Perimeter of the rectangle is

(a) 12 units
(b) 26 units
(c) 24 units
(d) 36 units

Q. The length of the parallel sides of a trapezium is in the ratio 10: 13 and the distance between them is 25 cm. If the area of trapezium is 655 cm², find the length of the parallel sides.

Q. What is the difference between parallelogram and rhombus?

Q.

If the perimeter of a regular hexagon is $66cm$, then its each side is equal to _______________.

Q.

Area of a circle whose radius is 5 cm is

1. 25π

2. 2π

3. 5π

4. 10π

Q.

If the circumference of a circle is 49.5meters more than its diameter, find the diameter of the circle .b(assume π = 22/7 )