Volume and Surface Area problems
- 1. How many cubes of 10cm edge can be put in a cubical box of 1m edge
Options- A. 10
- B. 100
- C. 1000
- D. 10000 Also asked in: Bank Exams, Bank PO
Correct Answer: 1000
Explanation:
Number of cubes= (100x100x100) / (10x10x10)= 1000
- 2. The surface area of a cube is 1734 sq. cm. Find its volume
Options- A. 2334 cubic.cm
- B. 3356 cubic.cm
- C. 4913 cubic.cm
- D. 3478 cubic.cm Discuss
Correct Answer: 4913 cubic.cm
Explanation:
Let the edge of the cube bea. Then,
6 = 1734
=> a = 17 cm.
Volume = = = 4193 cu.cm
- 3. The volume of a wall, 5 times as high as it is broad and 8 times as long as it is high, is 12.8 cu. meters. Find the breadth of the wall.
Options- A. 40cm
- B. 30cm
- C. 20cm
- D. 10cm Discuss
Correct Answer: 40cm
Explanation:
Let the breadth of the wall be x metres.
Then, Height = 5x metres and Length = 40x metres.
x * 5x * 40x = 12.8
=>
=> x = 4/10 m
=> x = (4/10)*100 = 40 cm
- 4. The diagonal of a rectangle is sqrt(41) cm. and its area is 20 sq. cm. The perimeter of the rectangle must be:
Options- A. 9 cm
- B. 18 cm
- C. 20 cm
- D. 41 cm Discuss
Correct Answer: 18 cm
Explanation:
= =40
Also, lb=20
= 41 + 40 =81
(l + b) = 9.
Perimeter = 2(l + b) = 18 cm.
- 5. The diagonal of a cube is 63 cm. Find its surface area
Options- A. 216 sq.cm
- B. 316 sq.cm
- C. 416 sq.cm
- D. 516 sq.cm Discuss
Correct Answer: 216 sq.cm
Explanation:
Let the edge of the cube be a.
so, the diagonal a =
=> a=6
Surface area = = 6 x 6 x 6 = 216 sq.cm
- 6. Three solid cubes of sides 1 cm, 6 cm and 8 cm are melted to form a new cube. Find the surface area of the cube so formed
Options- A. 486
- B. 586
- C. 686
- D. 786 Discuss
Correct Answer: 486
Explanation:
Volume of new cube = =
Edge of new cube = = 9cm
Surface area of the new cube = ( 6 x 9 x 9) sq.cm = 486 sq.cm
- 7. The dimensions of an open box are 50 cm, 40 cm and 23 cm. Its thickness is 2 cm. If 1 cubic cm of metal used in the box weighs 0.5 gms, find the weight of the box.
Options- A. 8.04kg
- B. 8.14kg
- C. 8.24kg
- D. 9.04kg Discuss
Correct Answer: 8.04kg
Explanation:
Volume of the metal used in the box = External Volume - Internal Volume
= [(50 x 40 x 23) - (44 x 34 x 20)] cu.cm
= 16080 cu.cm
Weight of the metal =[(16080 x 0.5)/1000] kg = 8.04 kg.
- 8. A town has a population of 4000 requires 140 liters of water per head. It has a tank measuring 18m x 12m x 8m. The water of this tank will suffice for ____ days?
Options- A. 3
- B. 4
- C. 5
- D. 2 Also asked in: AIEEE, Bank Exams, CAT, GATE, Bank Clerk, Bank PO
Correct Answer: 3
Explanation:
Water required = 4000 x 140 = 560000 lit = 560 cu.m (1 cu.m = 1000 lit)
Volume of tank = 18 x 12 x 8 = 1728 cu.m
Water of this tank will suffice for = 1728/560 = 3 days.
- 9. 50 men took a dip in a water tank 40 m long and 20 m broad on a religious day. If the average displacement of water by a man is 4 cu.m , then the rise in the water level in the tank will be:
Options- A. 20 cm
- B. 25 cm
- C. 35 cm
- D. 50 cm Discuss
Correct Answer: 25 cm
Explanation:
Total volume of water displaced =(4 x 50) cu.m = 200 cu.m
Rise in water level = =0.25m = 25cm
- 10. The size of the wooden block is 5 x 10 x 20 cm .How many such blocks will be required to construct a solid wooden cube of minimum size?
Options- A. 6
- B. 8
- C. 12
- D. 16 Also asked in: Bank Exams, Bank PO
Correct Answer: 8
Explanation:
Side of smallest cube = L.C.M of 5, 10, 20 = 20cm
Volume of the cube = (20 x 20 x 20)cu.cm = 8000 cu.cm
Volume of the block= (5 x 10 x 20)cu.cm = 1000 cu.cm
Number of blocks = (8000/1000) = 8
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