Exercise 7.4: Multiple choice questions

Mensuration

Exercise 7.4

Multiple choice questions

1. The semi-perimeter of a triangle having sides 15 cm, 20 cm and 25 cm is

(1) 60 cm

(2) 45 cm

(3) 30 cm

(4) 15 cm

Solution:

 s = [15+20+25] / 2 = 60/2 = 30

 [Answer: (3) 30 cm]

2. If the sides of a triangle are 3 cm, 4 cm and 5 cm, then the area is

(1) 3 cm²

(2) 6 cm²

(3) 9 cm²

(4) 12 cm²

Solution:

 s = 3+4+5 /2 = 12/2=6

A = √[6(6 − 3)(6 − 4)(6 − 5)] = √[6 × 3 × 2 × 1] = √36 = 6 sq. cm

[Answer: (2) 6 cm²]

3. The perimeter of an equilateral triangle is 30 cm. The area is

(1) 10√3 cm²

(2) 12√3 cm²

(3) 15√3 cm²

(4) 25√3 cm²

Solution:

3a=30

a = 10 cm

 A = √3/4 a² =  âˆš3/4 × 10 × 10 = 25√3 cm²

[Answer: (4) 25√3 cm²]

4. The lateral surface area of a cube of side 12 cm is

(1) 144 cm²

(2) 196 cm²

(3) 576 cm²

(4) 664 cm²

Solution:

4a² = 4×12×12 = 4×144=576 cm²

[Answer: (3) 576 cm²]

5. If the lateral surface area of a cube is 600 cm², then the total surface area is

(1) 150 cm²

(2) 400 cm²

(3) 900 cm²

(4) 1350 cm²

Solution:

4a² =600 cm²

6a² = [6 × 600 ] /4

6a² = 900

[Answer: (3) 900 cm²]

6. The total surface area of a cuboid with dimension 10 cm × 6 cm × 5 cm is

(1) 280 cm²

(2) 300 cm²

(3) 360 cm²

(4) 600 cm²

Solution:

TSA = 2 (lb + bh + hl)

= 2 (10 × 6 + 6 × 5 + 5 × 10) = 2 (60 + 30 + 50) = 2 (140) = 280 cm²

[Answer: (1) 280 cm²]

7. If the ratio of the sides of two cubes are 2:3, then ratio of their surface areas will be

(1) 4:6

(2) 4:9

(3) 6:9

(4) 16:36

Solution:

a:b = 2:3

4a²:4b² = 4×2²:4×3²

16:36

4:9

[Answer: (2) 4:9]

8. The volume of a cuboid is 660 cm³ and the area of the base is 33 cm². Its height is

(1) 10 cm

(2) 12 cm

(3) 20 cm

(4) 22 cm

Solution:

V = 660 cm³

lb = 33 cm²

h = ?

lbh = 660

h = 660 /33 = 20

[Answer: (3) 20 cm]

9. The capacity of a water tank of dimensions 10 m × 5 m × 1.5 m is

(1) 75 litres

(2) 750 litres

(3) 7500 litres

(4) 75000 litres

Solution:

Volume of cuboid = l × b × h

[Answer: (3) 7500 litres]

10. The number of bricks each measuring 50 cm × 30 cm × 20 cm that will be required to build a wall whose dimensions are 5 m × 3 m × 2 m is

(1) 1000

(2) 2000

(3) 3000

(4) 5000

Solution:

500×300×200 / 50×30×20 = 1000

[Answer: (1) 1000]