Volume and Surface Area problems
- 1. 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
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
- 2. 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
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
- 3. 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
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]
- 4. 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
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
- 5. 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
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
- 6. Water flows into a tank 100 m x 150 m x 2 m through a rectangular pipe 1.5 m x 1.25 m at a speed of 20 km/h. In what time, will the water rise by 2 m?
Options- A. 96 min
- B. 50 min
- C. 48 min
- D. 75 min Discuss
Correct Answer: 48 min
Explanation:
Volume of water in the tank = 100 x 500 x 2 = 30000 m3
Speed of water = 20 x 1000/60 = 1000/3 m/min
water flow per minute = (15/10) x (125/100) x (1000/3) = 625 m3
Time taken = 30000/625 = 48 min
- 7. A hospital room is to accommodate 56 patients. It should be done in such a way that every patient gets 2.2 m 2 of floor and 8.8 3 of space. If the length of the room is 14 m, then breadth and height of the room are respectively?
Options- A. 8.8 m, 4 m
- B. 8.4 m, 4.2 m
- C. 8 m, 4 m
- D. 7.8 m, 4.2 m Discuss
Correct Answer: 8.8 m, 4 m
Explanation:
Let the breadth and height of room be m and h m, respectively.
Then, according to the question, l x b = n x Area occupied by one patient
? 14 x b = 56 x 22
? b = (56 x 22)/14 = 8.8 m3
? h x Area of occupied by one patient = 8.8
h = 8.8/2.2
h = 4 m
- 8. A right circular metal cone (solid) is 8 cm high and the radius is 2 cm. It is metaled and recast into a sphere. What is the radius of the sphere?
Options- A. 2 cm
- B. 3 cm
- C. 4 cm
- D. 5 cm Discuss
Correct Answer: 2 cm
Explanation:
Given that, the height and radius of a right circular ,etal cone (solid) are 8 cm and 2 cm, respectively.
i.e., h = 8 cm and r = 2 cm
Let the radius of the sphere is R
Then, by condition,
1/3 ? r2 h = 4/3 ? R3 h
? 4 x 8 = 4 R3
? R3 = (2)3 = ? R = 2
? Radius odf the sphere = 2 cm
- 9. A cone has height which is half of 16.8 cm, while diameter of its base is 4.2 cm. It is melted and recast into a sphere. Find the surface area of the sphere.?
Options- A. 55.44 sq cm
- B. 60 sq cm
- C. 65.58 sq cm
- D. 59 sq cm Discuss
Correct Answer: 55.44 sq cm
Explanation:
Given that, Height = 1 m
Diameter = 140 cm or 140/100 m = 1.40 m
? r = 1.40/2 = 0.7 m
Now,
Required sheet = Total surface area = 2?r( h + r)
= (22/7) x 1.4 x (1 + 0.7) = 7.48 sq m
? Sheet required = 7.48 sq m
- 10. A cylindrical box of radius 5 cm contains 10 solid spherical balls, each of radius 5 cm. If the top most ball touches the upper cover of the box, then volume of the empty space in the box is?
Options- A. 2500/3 ? cm3
- B. 50000 ? cm3
- C. 2500 ? cm3
- D. 5000/3 ? cm3 Discuss
Correct Answer: 2500/3 ? cm3
Explanation:
Height of the cylinder = 10 x Diameter of each ball
= 10 x 10 = 100 cm
? Required empty space
= ? (5)2 (100) - 4/3 ? (5)3 x 10
= ? (5)2 x 10 [10 - 20/3]
= ? (5)2 x 10 [30 - 20/3] = 2500/3 ? cm3
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