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Volume and Surface Area
1.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:

Answer:Option 1

Explanation:

Solution:

Volume and Surface Area mcq solution image

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2.In a shower, 5 cm of rain falls. The volume of water that falls on 1.5 hectares of ground is:

Answer:Option 1

Explanation:

Solution:
1hectare=10000m2So,Area=(1.5×10000)m2=15000m2Depth=5100m=120mVolume=(Area×Depth)=(15000×120)m3=750m3

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3.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:

Answer:Option 1

Explanation:

Solution:
2(15+12)×h=2(15×12)h=18027m=203mVolume=(15×12×203)m3=1200m3

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4.A hollow iron pipe is 21 cm long and its external diameter is 8 cm. If the thickness of the pipe is 1 cm and iron weighs 8 g/cm3, then the weight of the pipe is:

Answer:Option 1

Explanation:

Solution:
Externalradius=4cmInternalradius=3cmVolumeofiron=(227×[(4)2(3)2]×21)cm3=(227×7×1×21)cm3=462cm3Weightofiron=(462×8)gm=3696gm=3.696kg

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5.A boat having a length 3 m and breadth 2 m is floating on a lake. The boat sinks by 1 cm when a man gets on it. The mass of the man is:

Answer:Option 1

Explanation:

Solution:
Volume of water displaced
= (3 x 2 x 0.01) m3
= 0.06 m3.
∴ Mass of man = Volume of water displaced x Density of water
= (0.06 x 1000) kg
= 60 kg.

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6.50 men took a dip in a water tank 40 m long and 20 m broad on a religious day. If the average displacement of water by a man is 4 m3, then the rise in the water level in the tank will be:

Answer:Option 1

Explanation:

Solution:
TotalVolumeofwaterdisplaced=(4×50)m3=200m3Riseinwaterlevel=(20040×20)m=0.25m=25cm

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7.The slant height of a right circular cone is 10 m and its height is 8 m. Find the area of its curved surface.

Answer:Option 1

Explanation:

Solution:
l=10mh=8mSo,r=l2h2=(10)282=6mCurvedsurfaceareaπrl=(π×6×10)m2=60πm2

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8.A metallic sheet is of rectangular shape with dimensions 48 m x 36 m. From each of its corners, a square is cut off so as to make an open box. If the length of the square is 8 m, the volume of the box (in m3) is:

Answer:Option 1

Explanation:

Solution:
Clearly, l = (48 - 16)m = 32 m,
b = (36 -16)m = 20 m,
h = 8 m.
∴ Volume of the box = (32 x 20 x 8) m3 = 5120 m3.

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9.The curved surface area of a cylindrical pillar is 264 m2 and its volume is 924 m3. Find the ratio of its diameter to its height.

Answer:Option 1

Explanation:

Solution:
πr2h2πrh=924264r=(924264×2)=7mAnd,2πfh=264h=(264×722×12×17)=6mRequiredratio=2rh=146=7:3

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10.A cistern of capacity 8000 litres measures externally 3.3 m by 2.6 m by 1.1 m and its walls are 5 cm thick. The thickness of the bottom is:

Answer:Option 1

Explanation:

Solution:
LetthethicknessofthebottombexcmThen,[(33010)×(26010)×(110x)]=8000×1000320×250×(110x)=8000×1000(110x)=8000×1000320×250=100x=10cm=1dm

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