Discussion
Home ‣ Aptitude ‣ Volume and Surface Area Comments
- Question
- A cylindrical jar, whose base has a radius of 15 cm, is filled with water upto a height of 20 cm, A solid iron spherical ball of radius 10 cm is dropped in the jar to submerge completely in water. Find the increase in the level of water (in cm).?
Options- A. 517/27
- B. 55/7
- C. 58/9
- D. 525/27
- Correct Answer
- 525/27
ExplanationLet level of water will be increased by h cm
? x (15)2 x h = (4/3)?(10)3
? h = [(4/3) x 10 x 10 x 10] / [15 x 15]
= 525/27 cm - 1. Water flows at the rate of 10 m/min from a cylindrical pipe 5 mm in diameter. How long will it take to fill up a conical vessel whose diameter at the base is 40 cm and depth is 24 cm?
Options- A. 51 min 12 s
- B. 52 min 1 s
- C. 48 min 15 s
- D. 55 min Discuss
- 2. In a shower, 10 cm of rain falls, What will be the volume of water that falls on 1 hect area of ground?
Options- A. 500 cm3
- B. 650 cm3
- C. 1000 cm3
- D. 750 cm3 Discuss
- 3. Seven equal cubes each of side 5 cm are joined end-to-end. Find the surface area of the resulting cuboid .?
Options- A. 750 sq cm
- B. 1500 sq cm
- C. 2250 sq cm
- D. 700 sq cm Discuss
- 4. The volume of a cuboid is twice the volume of a cube. If the dimensions of total cuboid are 9 cm, 8 cm and 6 cm, then total surface area of the cube will be?
Options- A. 213 sq cm
- B. 216 sq cm
- C. 218 sq cm
- D. 219 sq cm Discuss
- 5. The radius of a sphere and a right circular cylinder are equal and their curved surface areas are also equal. The ratio of their volumes is?
Options- A. 3 : 4
- B. 2 : 3
- C. 3 : 2
- D. 4 : 3 Discuss
- 6. A conical flask is full of water. The flask has base radius r and height h, This water is poured into a cylindrical flask of base radius mr. The height of water in the cylindrical flask is?
Options- A. h/2 m2
- B. 2h/m
- C. h/3m2
- D. m/2h Discuss
- 7. A hemispherical basin of 150 cm diameter holds water 120 times as much as a cylindrical tube. If the height of the tube is 15 cm, then the diameter of the tube is?
Options- A. 27 cm
- B. 24 cm
- C. 25 cm
- D. 26 cm Discuss
- 8. A copper sphere of diameter 36 cm is drawn into a wire of diameter 4 mm. Find the length of the wire.?
Options- A. 2000 m
- B. 15000 m
- C. 1855 m
- D. 1944 m Discuss
- 9. Find the area of the iron sheet required to prepare a cone double the height of 12 cm with diameter of the base 14 cm.?
Options- A. 504 sq cm
- B. 804 sq cm
- C. 304 sq cm
- D. 704 sq cm Discuss
- 10. What part of a ditch 48 m long, 16.5 m broad and 4 m deep can be filled by the earth got by digging a cylindrical tunnel of diameter 4 m and length 56 m?
Options- A. 1/9
- B. 2/9
- C. 7/9
- D. 8/9 Discuss
Volume and Surface Area problems
Search Results
Correct Answer: 51 min 12 s
Explanation:
Given, radius of pipe 5/2 x 10 = 5/20 cm [? 1 cm = 10 mm]
Height of pipe = 1000 cm
Radius of vessel = 20 cm and height = 24 cm
Volume of water flow in one minute from cylindrical pipe = ? (5/20)2 x 1000
= 125/2 ? cm3
and volume of conical vessel = 1/3 ?(20)2 x 24 = 3200? cm3
? Required time = (3200? x 2) / 125?
= 511/5 or 51 min 12 s
Correct Answer: 1000 cm3
Explanation:
1 hec = 10000 m3
Volume of water = Base area x Height
= (10000 x 10)/100 = 1000 m3
Correct Answer: 750 sq cm
Explanation:
Given, l = Length of the cuboid = 5 x 7 = 35 cm
h = Breadth of the cuboid = 5 cm
h = Height of the cuboid = 5 cm
? Surface area = 2(lb + bh + lh) = 2[35 x 5 + 5 x 5 + 35 x 5]
= 2[175 + 25 + 175]
= 2 x 375 = 750 sq cm
Correct Answer: 216 sq cm
Explanation:
Volume of the cuboid = 9 x 8 x 6 = 432 cm3
Volume of the cube = 1/2 x 432 = 216 cm3
? Each side of cube = ?216 = 6 cm
Total surface area of the cube = 6 x (Side)2 = 6 x 62
= 6 x 36 = 216 sq cm
Correct Answer: 2 : 3
Explanation:
Given, 4?r2 = 2?rh
? h = 2r
Now, required ratio
= 4/3?r3 : ?r2h
= 4r : 3h
= 4r : 6r [ ? h = 2r]
= 2 : 3
Correct Answer: h/3m2
Explanation:
Volume of water = Volume of conical flask = (1/3)?r2h
Now, the water is poured into cylindrical flask.
? Volume of cylinder = Volumes of water
? ? (mr)2 x Height = (1/3)?r2h
? Height = h/3m2
Correct Answer: 25 cm
Explanation:
Given, diameter = 150 cm
? r = 150/2 cm
According to the question,
2/3? (150/2)3 = 120 ?r2 x 15
? (2/3) x 150 x 150 x 150 / 8 = 120 x 15 x r2
? r2 = (150 x 150 x 150) / (12 x 120 x 5)
? r2 = 625/4
? r = ?625/4 = 25/2
? Diameter = 2r = 2 x 25/2 = 25 cm
Correct Answer: 1944 m
Explanation:
Let length of the wire be h According to the question,
Volume of sphere = Volume of wire
(4/3) x ? x 18 x 18 x 18 = ? x (2/10) x (2/10) x h
? h = (100 x 1944) cm
= (100 x 1944)/100 m = 1944 m [? 1 cm = 1/100 m]
Correct Answer: 704 sq cm
Explanation:
r = Radius of the cone = 14/2 = 7 cm
h = Height of the cone = 12 x 2 = 24 cm
? Slant height (l) = ?r2 + h2
= ?(7)2 + (24)2
= ?49 + 576
= ?625
= 25 cm
Area of the sheet = Total surface area
= (?rl + ?r2)
= ?r(l + r)
= (22/7) x 7 x (25 + 7) = 704 sq cm
Correct Answer: 2/9
Explanation:
Volume of the earth dugout as a tunnel = ?r2h = (22/7) x 2 x 2 x 56 = 704 m3
Volume of the ditch = (48 x 33)/(2 x 4) = 24 x 33 x 4 = 3168 m3
? Part required = 704/3168 = 2/9
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