1. Given a cylindrical tank, in which situation will you find surface area 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.
Answer: (a) We need to calculate the volume to find the capacity
(b) As plastering will cover the surface so we need surface area to know this
(c) Volume will give the capacity and that can be compared with capacity of smaller tanks
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?
Answer: As cylinder A’s radius is half of radius of cylinder B so its volume will be lesser than that of cylinder B. Although Cylinder B’s height is half of height of cylinder A but as you know while calculating the volume we need to square the radius so halving the radius has a greater impact than halving the height.
While calculating surface area, the curved surface area in both will be same and the total surface area will be greater in the cylinder with the greater radius.
3. Find the height of a cuboid whose base area is 180 cm2 and volume is 900 cm3?
Answer: Volume = Base Area x Height
4. A cuboid is of dimensions 60 cm Ã— 54 cm Ã— 30 cm. How many small cubes with side 6 cm can be placed in the given cuboid?
5. Find the height of the cylinder whose volume is 1.54 mÂ³ and diameter of the base is 140 cm ?
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 litres that can be stored in the tank?
As we know, 1 cubic metre = 1000 litres
So, 49.5 cubic metre = 49500 litres
7. If each edge of a cube is doubled,
(i) how many times will its surface area increase?
(ii) how many times will its volume increase?
Answer: (i) Whenever sides are doubled in any structure then area becomes 4 times the original structure
(ii) Volume becomes 8 times of the original volume if sides are doubled in any structure
8. Water is pouring into a cubiodal reservoir at the rate of 60 litres per minute. If the volume of reservoir is 108 mÂ³, find the number of hours it will take to fill the reservoir.
Answer: 108 cubic metre = 108000 litre
So, time = Volume Rate per minute
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