Inner radius of an hemispherical bowl is 18 cm. Bowl is filled with certain liquid and this liquid is poured into small cylindrical bottles. If diameter of base of each bottle is 6 cm and height is 4 cm, then how many bottles are required ?
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Solution
Let number of bottles required are = x
n × π ×
n = 108
Water pond is 50 m long and 16 m wide. 50 persons dip in it. If each person displaces 2 m3 of water, then find the increase in the level of water.
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Solution
Area of pond = 50 × 16 = 800 m2
Let increase in water level = 'h' m
Volume of water displaced = 50 × 2 = 100 m3
800 × h = 100
h =
h = 12.5 cm
A hemispherical bowl is made of 1 cm thick steel. If Inner radius of bowl is 4 cm, then How much volume of steel was used to made this bowl?
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Solution
Steel used =
=
=
=
= 127.80 cm3
Volume of a cuboid is 192000 cm3. Ratio of its sides are 4 : 3 : 2. Find the length of largest side.
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Solution
Let length = 4x
Breadth = 3x
height = 2x
Volume = 4x(3x) (2x)
24x3 = 192000
x3 = 8000
x = 20
Largest side = 4x
= 4 × 20 = 80 cm
A solid sphere of radius 13 cm is being melted into a cone of same base radius. Find the height of cone.
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Solution
Let height of cone = h
radius = r
Volume of sphere = volume of cone
h = 4r
h = 13 × 4 = 52 cm
A pond whose length, breadth and height are 4m, 2.5 m and 1.5 m respectively, has been dug in a 15 m long and 14 m wide field. Earth dug out from it, is evenly spread on the remaining field. Find the increase in height of surface of field.
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Solution
Area of field = 14 × 15 = 210 m2
Volume of earth dug out = 4 × 2.5 × 1.5 = 15 m3
Remaining Area of field = 210 – (4 × 2.5)
= 200 m2
Increase in height = m
= cm
= 7.5 cm
A room is 16m long, 5 m broad and 3 m high. How many persons can sit in the room if a person occupies 2.4 m3 of space ?
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Solution
Number of persons =
=
= = 100
Sum of length, breadth and height of a cuboid is 12 cm and length of its diagonal is 5 cm. Find its total surface area.
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Solution
l + b + h = 12 cm .......(i)
l2 + b2 + h2 = 50 .......(ii)
(l + b + h)2 = l2 + b2 + h2 + 2 (lb + bh + hl)
(12)2 = 50 + 2 (lb + bh + hl)
Total surface Area = 144 – 50 = 94 cm2
Curved surface area of a cylinder is 792 m2 and its volume is 2376 m3. Find the ratio between its diameter and height.
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Solution
Let radius of cylinder = r
Height = h
Curved surface area = 2πrh = 792 .......(i)
Volume = πr2h = 2376 .......(ii)
eq. (ii) ÷ (i)
r = 6 m
From (i)
h = 21 m.
Required ratio 2 × 6 : 21
12 : 21
4 : 7
Ratio between length, breadth and height of a cuboid is 2 : 5 : 7. If its total surface area is 4248 cm2, then find its volume.
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Solution
Let length of cuboid = 2x
Breadth = 5x
height = 7x
Total surface area = 2 [2x × 5x + 5x × 7x + 7x × 2x]
118x2 = 4248
x2 = 36
x = 6
Volume = [2(6) × 5(6) × 7(6)]
= 15120 cm3