1.Given a cylindrical tank, in which situation will you find surface are and in which situation volume.
(a) To find how much it can hold.
(b) Number of cement bags required to plaster it.
(c) To find the number of smaller tanks that can be filled with water from it.
Solution:
(a) In this situation, we can find the volume.
(b) In this situation, we can find the surface area.
(c) In this situation, we can find the volume.
2. Diameter of cylinder A is 7 cm and the height is 14 cm. Diameter of cylinder B is 14 cm and height is 7 cm. Without doing any calculations can you suggest whose volume is greater? Verify it by finding the volume of both the cylinders. Check whether the cylinder with greater volume also has greater surface area.
Solution:
Yes, we can say that volume of cylinder B is greater
Verification:
We have to find Volume for cylinders A and B
Now,
Diameter of cylinder A = 7 cm
Radius of cylinder A = 7/2 cm
And Height of cylinder A = 14 cm
Volume of cylinder A = πr2h
= (22/7 )×(7/2)×(7/2)×14 = 539
Volume of cylinder A is 539 cm3
Now,
Diameter of cylinder B = 14 cm
Radius of cylinder B = 14/2 = 7 cm
And Height of cylinder B = 7 cm
Volume of cylinder B = πr2h
= (22/7)×7×7×7 = 1078
Volume of cylinder B is 1078 cm3
Now, according to question:
We have to find surface area for cylinders A and B
Surface area of cylinder A = 2πr(r+h )
= 2 x 22/7 x 7/2 x (7/2 + 14) = 385 cm2
Surface area of cylinder B = 2πr(r+h)
= 2×(22/7)×7(7+7) = 616 cm2
Hence, cylinder B has greater surface area.
3. Find the height of a cuboid whose base area is 180 cm2 and volume is 900 cm3?
Solution:
Given,
Base area of cuboid = 180 cm2
Volume of cuboid = 900 cm3
Volume of cuboid = lbh
900 = 180×h
h= 900/180 = 5
Hence, the height of cuboid is 5 cm.
4. A cuboid is of dimensions 60 cm×54 cm×30 cm. How many small cubes with side 6 cm can be placed in the given cuboid?
Solution:
Given,
Length of cuboid (l) = 60 cm
Breadth of cuboid (b) = 54 cm
Height of cuboid (h) = 30 cm
Volume of cuboid = lbh
= 60 ×54×30
= 97200 cm3
Volume of cube = (Side)3
= 6×6×6 = 216 cm3
Also,
Number of small cubes = volume of cuboid / volume of cube
= 97200/216
= 450
Hence, required number of cubes are 450.
5. Find the height of the cylinder whose volume if 1.54 m3 and diameter of the base is 140 cm.
Solution:
Given:
Volume of cylinder = 1.54 m3
Diameter of cylinder = 140 cm
So, radius (r)= d/2 = 140/2 = 70 cm
Volume of cylinder = πr2h
1.54 = (22/7)×0.7×0.7×h
h = (1.54×7)/(22×0.7×0.7)
h = 1
Hence, height of the cylinder is 1 m.
6. A milk tank is in the form of cylinder whose radius is 1.5 m and length is 7 m. Find the quantity of milk in liters that can be stored in the tank.
Solution:
Given,
Radius of cylindrical tank (r) = 1.5 m
Height of cylindrical tank (h) = 7 m
Volume of cylindrical tank, V = πr2h
= (22/7)×1.5×1.5 ×7
= 49.5 cm3
= 49.5×1000 liters
= 49500 liters [1 m3= 1000 liters]
Hence, required quantity of milk is 49500 liters.
7. If each edge of a cube is doubled,
(i) how many times will its surface area increase?
Solution:
Let the edge of cube be “l”.
Surface area of the cube, A = 6 l2
When edge of cube is doubled,
Surface area of the cube, let A’ = 6(2l)2 = 6×4l2 = 4(6 l2)
A’ = 4A
Hence, surface area will increase by four times.
(ii)how many times will its volume increase?
Solution:
Volume of cube, V = l3
When edge of cube is doubled,
Volume of cube, let V’ = (2l)3 = 8(l3)
V’ = 8×V
Hence, volume will increase 8 times.
8. Water is pouring into a cuboidal reservoir at the rate of 60 liters per minute. If the volume of reservoir is 108 m3, find the number of hours it will take to fill the reservoir.
Solution:
Given,
volume of reservoir = 108 m3
Rate of pouring water into cuboidal reservoir = 60 liters/minute
= 60/1000 m3per minute
We know, 1 liter = (1/1000) m3
= (60×60)/1000 m3 per hour
Now,
(60×60)/1000 m3 water filled in reservoir will take = 1 hour
1 m3 water filled in reservoir will take = 1000/ (60×60) hours
So, 108 m3 water filled in reservoir will take = (108×1000)/(60×60) hours
= 30 hours
Hence, It will take 30 hours to fill the reservoir.
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