Mensuration Practice Questions

1) Question: If the surface area of the sphere is 616 cm2 and the radius of the sphere is equal to the radius of the cylinder. If the height of the cylinder is 12 cm, then what is the curved surface area of the cylinder?

A.528 cm2
B.548 cm2
C.538 cm2
D.518 cm2

Answer: A

Solution: 

The surface area of the sphere = 4πr2
4 * 22/7 * r * r = 616
r^2 = 49 => r = 7
The radius of the sphere = 7 cm
According to the question, the radius of the sphere and
cylinder is equal
So, the Radius of the cylinder = 7 cm
The curved surface area of the cylinder = 2πrh units^2
= 2 * 22/7 * 7 * 12 => 528
The curved surface area of the cylinder = 528 cm2

2) Question: Ratio of the breadth of the rectangle and side of the square is 5:8 and the perimeter of the square is 2 cm less than the perimeter of the rectangle. If the area of the rectangle is 276 cm2 less than that of the area of the square, then what is the area of the square?
A.225 cm2
B.576 cm2
C.484 cm2
D.Cannot be determined

Answer: D

Solution: 
Perimeter of the rectangle= 2 * (l + b)
Perimeter of the square = 4 * a
The breadth of the rectangle = 5x
Side of the square = 8x
2 * (l + 5x) – 4 * 8x = 2
2l – 22x = 2
l – 11x = 1 ----(1)
8x * 8x - l * 5x = 276
64x2 – 5xl = 276 ---(2)
From equation (1) and (2)
We cannot determine the area of the square.

3) Question: If the radius of the cylinder is equal to the radius of the circle whose area is 1386 cm 2 and the radius of the cylinder is 5% more than the height of the cylinder. What is 20% of the volume of the cylinder?
A.5644 cm3
B.5844 cm3
C.5244 cm3
D.5544 cm3

Answer: D

Solution: 
Area of the circle = πr2
22/7 * r * r = 1386
r^2 = 441 => r = 21
The radius of the circle = 21 cm
According to the question, the radius of the circle is
equal to the radius of the cylinder
The radius of the cylinder = 21 cm
Height of the cylinder = 21 * 100/105 = 20 cm
The volume of the cylinder of 20% = πr2h
= (22/7 * 21 * 21 * 20) * 20/100
= 5544 cm3

4) Question: The perimeter of the rectangular field is twice the perimeter of the square field. If one of the sides of the square field is 20m and the breadth of the rectangular field is 30m then find the area of the rectangular field.

A. 1250 sq m

B. 1500 sq.m

C. 1300 sq.m

D. 1350 sq.m

Answer: B

Solution: 

The perimeter of a square field = 20 * 4 = 80 m

The perimeter of a rectangular field = 160 m

Let the length of the rectangular field be x

160 = 2 ( x + 30 )

160 - 60 = 2x

x = 50 m

Area of the rectangular field = 50 * 30

= 1500 sq.m

5) Question: The total area of a circle and rectangle is 2058 sq cm. The radius of the circle is 21 cm. Find the perimeter of the rectangle, if the breadth of the rectangle is 24 cm.
A. 122 cm
B. 136 cm
C. 104 cm
D. 148 cm

Answer: C

Solution: 
Πr2 + lb = 2058
(22/7) * 21 * 21 + l * 24 = 2058
1386 + 24l = 2058
24l = 2058 - 1386
24l = 672
l = 28 cm
Perimeter of rectangle = 2 * (l + b) = 2 * (28 + 24)
=> 2 * 52 = 104 cm

6) Question: The perimeter of a rectangular field is thrice the perimeter of a square field. If one of the sides of the square field is 24 m and the breadth of the rectangular field is 48 m then find the area of the rectangular field.
A. 4276 sq m
B. 5354 sq m
C. 3892 sq m
D. 4608 sq m

Answer: D

Solution:
Perimeter of square field = 24 * 4 = 96 m
Perimeter of the rectangular field = 96 * 3 = 288 m
Let the length of the rectangular field be x
288 = 2 * (x + 48)
288 – 96 = 2x
x = 96 m
Area of the rectangular field = 96 * 48 = 4608 Sq. m

7) Question: The length of a rectangle is 16 m more than the side of the square and the breadth of the rectangle is 7m less than the side of the square. If the area of the square is 1156 Sq m. what is the area of the rectangle?
A. 1120 sq m
B. 1240 sq m
C. 1350 sq m
D. 1060 sq m

Answer: C

Solution:

Area of square = 1156 sq m
Side of the square = 34 m
Length of the rectangle = 34 + 16 = 50 m
Breadth of the rectangle = 34 – 7 = 27 m
Area of the rectangle = 50 * 27 = 1350 sq m

8) Question:  If the ratio of the height of the cylinder to the radius of the cylinder is 3:2 and the curved surface area of the cylinder is 1848 cm 2. If the radius of the cylinder is equal to the radius of the cone and the height of the cone is 9 cm, then what is the volume of the cone?
A.1448 cm3
B.1648 cm3
C.1948 cm3
D.1848 cm3

Answer: D

Solution: 
The curved surface area of the cylinder= 2πrh
The ratio of height to the radius of the cylinder = 3x: 2x
= 2 * 22/7 * 2x * 3x = 1848
X^2 = 49 => X = 7
Radius of the cylinder = 7 * 2 = 14 cm
According to the question, a radius of the cylinder and
cone is equal
The radius of the cone = 14 cm
The volume of the cone = 1/3πr2h
= 1/3 * 22/7 * r2 * h
=1/3 * 22/7 * 14 * 14 * 9 => 1848
Volume of the cone = 1848 cm3

9) Question: The perimeter of the rectangular field is 2 times the perimeter of the square field. If the side of the square field is 18 m and the length of the rectangular field is 45 m, then find the area of the rectangular field.
A. 1215 sq m
B. 1336 sq m
C. 1050 sq m
D. 1152 sq m 

Answer: A

Solution: 
Side of square (a) = 18 m
Perimeter of rectangle = 2 * 4a = 2 * 4 * 18 = 144
= > 2(b + 45) = 144
= > b + 45 = 72
= > b = 72 – 45 = 27 m
Area of rectangle = lb = 45 * 27 = 1215 sq m.

10) Question: The perimeter of the equilateral triangle is 54 cm. The side of the equilateral triangle is 3 cm less than the radius of the circle. Find the difference between the circumference of a circle and the perimeter of an equilateral triangle.
A. 78 cm
B. 84 cm
C. 88cm
D. 72 cm

Answer: A

Solution:
The perimeter of an equilateral triangle = 3a
3a = 54
Side (a) of the equilateral triangle = 18 cm
The side of the equilateral triangle = Radius of the circle – 3
Radius of circle = 18 + 3 = 21 cm
Circumference of circle = 2πr
= 2 * (22/7) * 21 = 132 cm
Required difference = 132 – 54 = 78 cm 

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