Volume and Surface Area problems
- 1. The cost of painting the four walls of a room is Rs. 350. The cost of painting a room three times in length, breadth and height respectively will be?
Options- A. Rs. 1050
- B. Rs. 1400
- C. Rs. 3150
- D. Rs. 4200 Discuss
Correct Answer: Rs. 3150
Explanation:
Area of 4 walls of the room = [2 (l + b ) x h ]m2
Area of 4 walls of new room = [2 (3l + 3b) x 3h]m2
= 9 x [2(l + b) x h ]m2
? Cost of painting the 4 walls of the new room = Rs. (9 x 350)
= Rs. 3150
- 2. A solid consists of a circular cylinder with an exact fitting right circular cone placed on the top. The height of the cone is h. If the total volume of the cone, then the height of the cylinder is?
Options- A. 2h
- B. 4h
- C. 2h/3
- D. 3h/2 ?r2 x 5 Discuss
Correct Answer: 2h/3
Explanation:
Let the height of the cylinder be H and its radius = r
Then, (?r2 H) + (1/3) x (?r2h) = 3 x (1/3)?r2h
? ?r2H = (2/3)?r2h
? H = 2h/3.
- 3. The diagonal of a cube is 2? 3 cm. Find the surface area of the cube.
Options- A. 15 sq cm
- B. 18 sq cm
- C. 25 sq cm
- D. 24 sq cm Discuss
Correct Answer: 24 sq cm
Explanation:
Given, diagonal = 2?3
? a?3 = 2?3 [a = edge of the cube]
? a = 2
? Required surface area = 6a2
= 6 x 22 = 24 sq cm
- 4. If the total surface area of a cube is 6 sq units, then what is the volume of the cube?
Options- A. 1 cu unit
- B. 2 cu units
- C. 4 cu units
- D. 6 cu units Discuss
Correct Answer: 1 cu unit
Explanation:
Total surface area of a cube = 6a2
? 6 = 6a2
? a2 = 1
? a = 1
Now, volume of the cube = a3 = 13 = 1 cu unit
- 5. If the volume of a cube is 729 cu cm, what is the length of its diagonal?
Options- A. 9?2 cm
- B. 9?3 cm
- C. 18 cm
- D. 18?3 Discuss
Correct Answer: 9?3 cm
Explanation:
Volume of cube = (Side)3
? 729 = a3
? a = 9 cm
Diagonal of cube = side x ?3 = 9 x ?3
= 9?3 cm
- 6. Find the surface area of a cuboid 10 m long, 5 m broad and 3 m high?
Options- A. 105 sq m
- B. 104 sq m
- C. 170 sq m
- D. 190 sq m Discuss
Correct Answer: 190 sq m
Explanation:
Given that, l = 10 m , b = 5 m, h = 3 m
lb = 10 x 5 = 50, bh = 5 x 3 = 15,
lh = 10 x 3 = 30
? Surface area of a cuboid
= 2(lb + bh + lh)
= 2(50 + 15 + 30)
= 2 x 95 = 190 sq m
- 7. The surface area of a cube is 726 sq cm. Find the volume of the cube.?
Options- A. 1331 cm3
- B. 1232 cm3
- C. 1626 cm3
- D. 1836 cm3 Discuss
Correct Answer: 1331 cm3
Explanation:
According to the question,
6a2 = 726 [a = edge of the cube]
? a2 = 726/6 = 121
? a = ?121 = 11 cm
? Required volume = a3 = 113 = 1331 cm3
- 8. The volume of a cuboid is 1989 cm 3 , while its length and breadth are 17 cm and 13 cm, respectively, Find the height of the cuboid.?
Options- A. 9 cm
- B. 4 cm
- C. 14 cm
- D. 7 cm Discuss
Correct Answer: 9 cm
Explanation:
Volume = 1989
? lbh = 1989
? 17 x 13 x h = 1989
? h = 1989/(17 x 17) = 9 cm
- 9. Three cubes of sides 1 cm, 6 cm and 8 cm are melted to form a new cube. Find half of the surface area of the new cube.?
Options- A. 243 sq cm
- B. 463 sq cm
- C. 486 sq cm
- D. 293 sq cm Discuss
Correct Answer: 243 sq cm
Explanation:
Volume (new cube) = (13 + 63 + 83 ) = 729 cm3
a3 = 729
? a = ? 729
? Surface area of the new cube = 6a2
= 6 x 92 = 486 sq cm
Surface area/2 = 486/2 = 243 sq cm
- 10. The maximum length of a pencil that can be kept in a rectangular box of dimensions 8 cm x 6 cm x 2 cm, is?
Options- A. 2?13 cm
- B. 2?14 cm
- C. 2?26 cm
- D. 10?2 cm Discuss
Correct Answer: 2?26 cm
Explanation:
Length of largest pencil that can be kept in a box
= Diagonal of box = ?l2 + b2 + h2
where, l = 8 cm, b = 6 cm , h = 2 cm
= ?64 + 36 + 4
= ?104 = 2?26
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