Mensuration Test

Result

Mensuration Test - 5

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Weekly Quiz Competition

Question 1
3 / -1

The radii of two spheres are in the ratio of 1 : 2. Find the ratio of their surface areas.

A
1 : 3

B
2 : 3

C
1 : 4

D
3 : 4

Solution
Question 2
3 / -1

Find the number of bricks, each measuring 25 cm × 12.5 cm × 7.5 cm, required to construct a wall 12 m long, 5 m high and 0.25 m thick, while the sand and cement mixture occupies 5% of the totalvolume of wall.

A
6080

B
3040

C
1520

D
12160

Solution

Volume of wall = 1200 × 500 × 25 = 15000000 cm³
Volume of cement = 5% of 15000000 = 750000 cm³
Remaining volume = 15000000 – 750000 = 14250000 cm³
Volume of a brick = 25 × 12.5 × 7.5 = 2343.75 cm³
Question 3
3 / -1

In a shower, 10 cm of rain falls. What will be the volume of water that falls on 1 hectare area ofground?

A
500 m³

B
650 m³

C
1000 m³

D
750 m³

Solution
Question 4
3 / -1

In a swimming pool measuring 90 m by 40 m, 150 men take a dip. If the average displacement of water by a man is 8 cubic metres, what will be rise in water level?

A
30 cm

B
50 cm

C
20 cm

D
33.33 cm

Solution

Let the rise in height be = h
Then, as per the question, the volume of water should be equal in both the cases.
Now, 90 × 40 × h = 150 × 8
Question 5
3 / -1

Two cones have their heights in the ratio 1 : 2 and the diameters of their bases are in the ratio 2 :1. What will be the ratio of their volumes?

A
4 : 1

B
2 : 1

C
3 : 2

D
1 : 1

Solution

If the ratio of their diameters = 2 : 1, then the ratio of their radii will also be = 2 : 1
Let the radii of the broader cone = 2 and height be = 1
Then the radii of the smaller cone = 1 and height be = 2
Question 6
3 / -1

A closed wooden box measures externally 10 cm long, 8 cm broad and 6 cm high. Thickness ofwood is 0.5 cm. Find the volume of wood used.

A
230 cubic cm

B
165 cubic cm

C
330 cubic cm

D
300 cubic cm.

Solution

Volume of wood used = External volume – Outer Volume
fi (10 × 8 × 6) – (10 – 1) × (8 – 1) × (6 – 1)
fi 480 – (9 × 7 × 5) = 165 cm²
Question 7
3 / -1

Three cubes each of volume of 216 m3 are joined end to end. Find the surface area of the resulting figure.

A
504 m²

B
216 m²

C
432 m²

D
480 m²

Solution

Let one side of the cube = a
Then a³ = 216 fi a = 6 m
Area of the resultant figure
= Area of all 3 cubes – Area of covered figure
fi 216 × 3 – (4 × a²) fi 648 – 144 fi 504 m²
Question 8
3 / -1

The largest cone is formed at the base of a cube of side measuring 7 cm. Find the ratio of volumeof cone to cube.

A
20 : 21

B
22 : 21

C
21 : 22

D
42 : 11

Solution
Question 9
3 / -1

Find the radius of the circle inscribed in a triangle whose sides are 8 cm, 15 cm and 17 cm.

A
4 cm

B
5 cm

C
3 cm

D
2√2 cm

Solution
Question 10
3 / -1

A cube whose edge is 20 cm long has circle on each of its faces painted black. What is the totalarea of the unpainted surface of the cube if the circles are of the largest area possible?

A
85.71 cm²

B
257.14 cm²

C
514.28 cm²

D
331.33 cm²

Solution

Surface area of the cube = 6a² = 6 × (20)²
= 2400
Area of 6 circles of radius 10 cm = 6pr²
= 6 × p × 100
= 1885.71
Remaining area = 2400 – 1884 = 514.28
Question 11
3 / -1

In the adjacent figure, find the area of the shaded region. (Use = 22/7)

A
15.28 cm²

B
61.14 cm²

C
30.57 cm²

D
40.76 cm²

Solution
Question 12
3 / -1

The perimeter of a sector of a circle of radius 5.7 m is 27.2 m. Find the area of the sector.

A
90.06 cm²

B
135.09 cm²

C
45 cm²

D
None of these

Solution

Let the angle subtended by the sector at the centre be = q
Then,
Question 13
3 / -1

A circular tent is cylindrical to a height of 3 metres and conical above it. If its diameter is 105 mand the slant height of the conical portion is 53 m, calculate the length of the canvas 5 m wide tomake the required tent.

A
3894

B
973.5

C
1947 m

D
1800 m

Solution
Question 14
3 / -1

If the curved surface area of a cone is thrice that of another cone and slant height of the secondcone is thrice that of the first, find the ratio of the area of their base.

A
81 : 1

B
9 : 1

C
3 : 1

D
27 : 1

Solution
Question 15
3 / -1

Two circles touch internally. The sum of their areas is 116p cm² and distance between theircentres is 6 cm. Find the radii of the circles.

A
10 cm, 4 cm

B
11 cm, 4 cm

C
9 cm, 5 cm

D
10 cm, 5 cm

Solution

Let the radius of the bigger circle = R
Let the radius of the smaller circle = r
Then as per question; R – r = 6
Solving through options; only option (a) satisfies this condition.