Volume and Surface Area of Solid Figures
- 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 ?
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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 = π (5/20)2 x 1000
= 125/2 π cm3
and volume of conical vessel = 1/3 π(20)2 x 24 = 3200π cm3
∴ Required time = (3200π x 2) / 125πCorrect Option: A
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 = π (5/20)2 x 1000
= 125/2 π cm3
and volume of conical vessel = 1/3 π(20)2 x 24 = 3200π cm3
∴ Required time = (3200π x 2) / 125π
= 511/5 or 51 min 12 s
- 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). ?
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Let level of water will be increased by h cm
π x (15)2 x h = (4/3)π(10)3Correct Option: D
Let level of water will be increased by h cm
π x (15)2 x h = (4/3)π(10)3
∴ h = [(4/3) x 10 x 10 x 10] / [15 x 15]
= 525/27 cm
- 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 ?
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Volume of water = Volume of conical flask = (1/3)πr2h
Now, the water is poured into cylindrical flask.
∴ Volume of cylinder = Volumes of water
⇒ π (mr)2 x Height = (1/3)πr2hCorrect Option: C
Volume of water = Volume of conical flask = (1/3)πr2h
Now, the water is poured into cylindrical flask.
∴ Volume of cylinder = Volumes of water
⇒ π (mr)2 x Height = (1/3)πr2h
∴ Height = h/3m2
- 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. ?
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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 = 2πr( h + r)Correct Option: A
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 = 2πr( h + r)
= (22/7) x 1.4 x (1 + 0.7) = 7.48 sq m
∴ Sheet required = 7.48 sq m
- A hospital room is to accommodate 56 patients. It should be done in such a way that every patient gets 2.2 m2 of floor and 8.83 of space. If the length of the room is 14 m, then breadth and height of the room are respectively ?
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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 = 8.8Correct Option: A
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
