Volume and Surface Area problems
- 1. A box is of 10 cm long, 8 cm broad and 5 cm high. What is the longest possible length of a pencil that can be put in?
Options- A. ?150 cm
- B. ?98 cm
- C. 3?21 cm
- D. 3?52 cm Discuss
Correct Answer: 3?21 cm
Explanation:
Since, the box is in the form of a cuboid.
? Required length = ?102 +82 + 52 cm
= ?189
= ?9 x 21
= 3?21 cm
- 2. What is the maximum number of pieces of 5cm x 5cm x 10 cm of cake that can be cut from a big cake of 5 cm x 30 cm x 30 cm size?
Options- A. 10
- B. 15
- C. 18
- D. 30 Discuss
Correct Answer: 18
Explanation:
Maximum number of pieces that can be cut out
= (Volume of cake) / (Volume of Each piece of cake)
= (5 x 30 x 30)/(5 x 5 x 10) = 18
- 3. Find the height of the cylinder whose volume is 551 m 3 and the area of the base is 36.5 m 2.?
Options- A. 7 m
- B. 10.5 m
- C. 14 m
- D. None of these Discuss
Correct Answer: 14 m
Explanation:
Volume of cylinder = ?r2= Area base x height
551 = 36.5 x h
h = 511/365 = 14 m
- 4. The length of the longest pole that can be placed in a room 12 m long and 9 m wide and 8 m high is?
Options- A. 12 m
- B. 14 m
- C. 17 m
- D. 21 m Discuss
Correct Answer: 17 m
Explanation:
Length of longer rod = ?l2 + b2 + h2
= ?122 + 92 + 82
= ?144 + 81 + 64
= ?289
= 17 m
- 5. The length of longest rod that can fit in a cubical vessel of side 10 cm, is?
Options- A. 10 cm
- B. 10?2
- C. 10?3
- D. None of these Discuss
Correct Answer: 10?3
Explanation:
Longest rod = ?(10)2 + (10)2 + (10)2 cm
=?300 cm
=10?3 cm
- 6. The length of longest rod that can be placed in a room 20 m long, 16 m broad and 12 m high, is?
Options- A. 20 m
- B. 16.4 m
- C. 48 m
- D. 28.2 m Discuss
Correct Answer: 28.2 m
Explanation:
Length of the rod = ?(20)2 + (16)2 + (12)2 m
= ?800 m
= 20?2 m
= (20 x 1.41) m
= 28.2 m
- 7. Half cubic meter of gold sheet is extended by hammering so as to cover an area of hectare. The thickness of the sheet is?
Options- A. 0.5 cm
- B. 0.05 cm
- C. 0.005 cm
- D. 0.0005 cm Discuss
Correct Answer: 0.005 cm
Explanation:
Thickness = Volume / Area
= (1/2)/10000 m
= (1 x 100)/(2 x 10000) cm
= 0.005 cm
- 8. In a shower, 5 cm of rain falls. The volume of water that falls on 2 hectare of ground, is?
Options- A. 100 m3
- B. 1000 m3
- C. 10 m3
- D. 10000 m3 Discuss
Correct Answer: 1000 m3
Explanation:
Volume = Area x Thickness of rainfall
= 2 x 10000 x (5/100) m3
= 1000 m3
- 9. The area of the base of a rectangular tank is 6500 sq. cm and the volume of water contained in it is 2.6 cubic meters. The depth of water is?
Options- A. 3.5 m
- B. 4 m
- C. 5 m
- D. 8 m Discuss
Correct Answer: 4 m
Explanation:
Let depth = D cm.
Then, D x 6500 = 2.6 x 100 x 100 x 100
? D = (2.6 x 100 x 100 x 100) / 6500 cm
= 400 cm = 4 cm
- 10. The number of small cubes with edges of 10 cm that can be accommodated in a cubical box 1 meter edge is?
Options- A. 10
- B. 100
- C. 1000
- D. 10000 Discuss
Correct Answer: 10000
Explanation:
Number of cubes = (100 x 100 x 100)/(10 x 10 x 10) = 1000
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