Volume and Surface Area problems
- 1. D and E are points on side AB and AC of ?ABC. DE is parallel to BC. If AD:DB = 2:3, what is the ratio of area of ?ADE and area of quadrilateral BDEC?
Options- A. 4 : 21
- B. 4 : 25
- C. 4 : 29
- D. 4 : 9 Discuss
Correct Answer: 4 : 21
- 2. 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
- 3. D and E are points on side AB and AC of ?ABC. DE is parallel to BC. If AD:DB = 2:3, what is the ratio of area of ?ADE and area of quadrilateral BDEC?
Options- A. 4 : 21
- B. 4 : 25
- C. 4 : 29
- D. 4 : 9 Discuss
Correct Answer: 4 : 21
- 4. If each edge of a cube is increased by 50%, find the percentage increase in Its surface area
Options- A. 125%
- B. 150%
- C. 175%
- D. 110% Discuss
Correct Answer: 125%
Explanation:
Let the edge = a cm
So increase by 50 % = a + a/2 = 3a/2
Total surface Area of original cube =
TSA of new cube = = =
Increase in area = =
Increase % = = 125%
- 5. How many cubes of 3cm edge can be cut out of a cube of 18cm edge
Options- A. 36
- B. 232
- C. 216
- D. 484 Also asked in: Bank Exams, Bank PO
Correct Answer: 216
Explanation:
number of cubes=(18 x 18 x 18) / (3 x 3 x 3) = 216
- 6. A right triangle with sides 3 cm, 4 cm and 5 cm is rotated the side of 3 cm to form a cone. The volume of the cone so formed is:
Options- A. 12 pi cub.cm
- B. 15 pi cub.cm
- C. 16 pi cub.cm
- D. 20 pi cub.cm Discuss
Correct Answer: 12 pi cub.cm
- 7. A rectangular block 6 cm by 12 cm by 15 cm is cut up into an exact number of equal cubes. Find the least possible number of cubes.
Options- A. 30
- B. 40
- C. 10
- D. 20 Discuss
Correct Answer: 40
Explanation:
Volume of the block = (6 x 12 x 15) cu.cm = 1080 cu.cm
Side of the largest cube = H.C.F. of 6 cm, 12 cm, 15 cm
= 3 cm.
Volume of this cube = (3 x 3 x 3) cu.cm = 27 cu.cm
Number of cubes = = 40.
- 8. A hall is 15 m long and 12 m broad. If the sum of the areas of the floor and the ceiling is equal to the sum of the areas of four walls, the volume of the hall is:
Options- A. 720
- B. 900
- C. 1200
- D. 1800 Discuss
Correct Answer: 1200
- 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
- B. 50
- C. 53.5
- D. 55 Discuss
Correct Answer: 49
Explanation:
Area of the wet surface = [2(lb + bh + lh) - lb]
= 2(bh + lh) + lb
= [2 (4 x 1.25 + 6 x 1.25) + 6 x 4]
= 49
- 10. How many bricks each measuring 25cm x 11.25cm x 6cm, will be needed to build a wall 8m x 6m x 22.5m
Options- A. 5600
- B. 600
- C. 6400
- D. 7200 Also asked in: Bank Exams, Bank PO
Correct Answer: 6400
Explanation:
No. of bricks= volume of the wall/volume of 1 brick
= (800 x 600 x 22.5) / (25 x 11.25 x 6) = 6400
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