Volume and Surface Area problems
- 1. The radius and height of a solid cylinder are increased by 2% each. What will be the approximate percentage increase in volume?
Options- A. 6.76
- B. 5.88
- C. 6.12
- D. 3.34 Also asked in: Bank Exams
Correct Answer: 6.12
- 2. A sphere of radius 21 cm is cut into 8 identical parts by 3 cuts (1 cut along each axis). What will be the total surface area (in cm2) of each part?
Options- A. 844.5
- B. 1732.5
- C. 1039.5
- D. 1115.6 Also asked in: Bank Exams
Correct Answer: 1732.5
- 3. The ratio between the length and the breadth of a rectangular park is 3 : 2. If a man cycling along the boundary of the park at the speed of 12 km/hr completes one round in 8 minutes, then the area of the park (in sq. m) is:
Options- A. 15360
- B. 153600
- C. .30720
- D. 307200 Discuss
Correct Answer: 153600
Explanation:
Perimeter = Distance covered in 8 min. = (12000/60) * 8 = 1600m
Let length = 3x metres and breadth = 2x metres.
Then, 2(3x + 2x) = 1600 or x = 160.
Length = 480 m and Breadth = 320 m.
Area = (480 x 320) = 153600
- 4. An error 2% in excess is made while measuring the side of a square. The percentage of error in the calculated area of the square is:
Options- A. 2%
- B. 2.02%
- C. 4%
- D. .4.04% Discuss
Correct Answer: .4.04%
Explanation:
100 cm is read as 102 cm.
A1 = (100 x 100) and A2 =(102 x 102)
(A2 - A1) = [(102 x 102)-(100 x 100) ]= 404
Percentage error =[404/(100 x 100 )] x 100%= 4.04%
- 5. The ratio between the perimeter and the breadth of a rectangle is 5 : 1. If the area of the rectangle is 216 sq. cm, what is the length of the rectangle?
Options- A. 16cm
- B. 18cm
- C. 24cm
- D. .Data inadequate Discuss
Correct Answer: 18cm
Explanation:
2(l+b)/b = 5/1
=> 2l + 2b = 5b
=> 3b = 2l
=> b =(2/3) x l
Then, Area = 216 sq.cm
l x b = 216
=> l x [(2/3)x l] =216
=> l x l = 324
=> l = 18 cm.
- 6. The difference between the length and breadth of a rectangle is 23 m. If its perimeter is 206 m, then its area is:
Options- A. 1520 sq.m
- B. 2420 sq.m
- C. 2480 sq.m
- D. 2520 sq.m Discuss
Correct Answer: 2520 sq.m
Explanation:
We have: (l - b) = 23 and 2(l + b) = 206 or (l + b) = 103.
Solving the two equations, we get: l = 63 and b = 40.
Area = (l x b) = (63 x 40) sq.m
= 2520 sq.m
- 7. The length of a rectangle is halved, while its breadth is tripled. What is the percentage change in area?
Options- A. 25% increase
- B. 50% increase
- C. 50% decrease
- D. 75% decrease Discuss
Correct Answer: 50% increase
Explanation:
Let original length = x and original breadth = y.
Original area = xy.
New length = x/2 and New breadth = 3y.
New area = (x/2 * 3y) = (3/2 )xy
Therefore, Increase % = [(1/2)xy * (1/xy) * 100] % = 50%
- 8. A tank is 25 m long, 12 m wide and 6 m deep. The cost of plastering its walls and bottom at 75 paise per sq. m, is:
Options- A. Rs. 456
- B. Rs. 458
- C. Rs. 558
- D. Rs. 568 Discuss
Correct Answer: Rs. 558
Explanation:
Area to be plastered= [2(l + b) x h] + (l x b)
= [2(25 + 12) x 6] + (25 x 12)
= (444 + 300)
= 744
Cost of plastering = Rs. 744 x (75/100)= Rs. 558
- 9. A cistern 6m long and 4 m wide contains water up to a depth of 1 m 25 cm. The total area of the wet surface is:
Options- A. 49 sq.m
- B. 50 sq.m
- C. 51 sq.m
- D. 52 sq.m Discuss
Correct Answer: 49 sq.m
- 10. A boat having a length 3 m and breadth 2 m is floating on a lake. The boat sinks by 1 cm when a man gets on it. The mass of the man is:
Options- A. 12
- B. 60
- C. 72
- D. 90 Discuss
Correct Answer: 60
Explanation:
Volume of water displaced = (3 x 2 x 0.01) = 0.06 cu.m.
Mass of man = Volume of water displaced x Density of water
= (0.06 x 1000) kg
= 60 kg.
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