11.
The curved surface area of a cylindrical pillar is 264 m2 and its volume is 924 m3. Find the ratio of its diameter to its height.
A. 3 : 7 B. 7 : 3
C. 6 : 7 D. 7 : 6
Answer & Explanation
Answer: Option B
Explanation:
r2h = 924 r = 924 x 2 = 7 m.
2rh 264 264
And, 2rh = 264 h = 264 x 7 x 1 x 1 = 6m.
22 2 7
Required ratio = 2r = 14 = 7 : 3.
h 6
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12.
A cistern of capacity 8000 litres measures externally 3.3 m by 2.6 m by 1.1 m and its walls are 5 cm thick. The thickness of the bottom is:
A. 90 cm B. 1 dm
C. 1 m D. 1.1 cm
Answer & Explanation
Answer: Option B
Explanation:
Let the thickness of the bottom be x cm.
Then, [(330 – 10) x (260 – 10) x (110 – x)] = 8000 x 1000
320 x 250 x (110 – x) = 8000 x 1000
(110 – x) = 8000 x 1000 = 100
320 x 250
x = 10 cm = 1 dm.
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13.
What is the total surface area of a right circular cone of height 14 cm and base radius 7 cm?
A. 344.35 cm2 B. 462 cm2
C. 498.35 cm2 D. None of these
Answer & Explanation
Answer: Option C
Explanation:
h = 14 cm, r = 7 cm.
So, l = (7)2 + (14)2 = 245 = 75 cm.
Total surface area = rl + r2
= 22 x 7 x 75 + 22 x 7 x 7 cm2
7 7
= [154(5 + 1)] cm2
= (154 x 3.236) cm2
= 498.35 cm2.
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14.
A large cube is formed from the material obtained by melting three smaller cubes of 3, 4 and 5 cm side. What is the ratio of the total surface areas of the smaller cubes and the large cube?
A. 2 : 1 B. 3 : 2
C. 25 : 18 D. 27 : 20
Answer & Explanation
Answer: Option C
Explanation:
Volume of the large cube = (33 + 43 + 53) = 216 cm3.
Let the edge of the large cube be a.
So, a3 = 216 a = 6 cm.
Required ratio = 6 x (32 + 42 + 52) = 50 = 25 : 18.
6 x 62 36
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15.
How many bricks, each measuring 25 cm x 11.25 cm x 6 cm, will be needed to build a wall of 8 m x 6 m x 22.5 cm?
A. 5600 B. 6000
C. 6400 D. 7200
Answer & Explanation
Answer: Option C
Explanation:
Number of bricks = Volume of the wall = 800 x 600 x 22.5 = 6400.
Volume of 1 brick 25 x 11.25 x 6