Mensuration

Exercise 11.4

Question 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.
Answer: Volume

(b) Number of cement bags required to plaster it.
Answer: Surface Area

Question 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.

Volume of cylinder `=πxx\r^2xx\h`

Volume of cylinder A `= (22)/(7)xx7/2xx7/2xx14=539` cubic cm

Volume of cylinder B `= (22)/(7)xx7xx7xx7=1078` cubic cm

Curved surface area of cylinder `=2πrh`

Curved surface area of cylinder A `=2xx(22)/(7)xx7/2xx14=308` sq cm

Curved surface area of cylinder B `=2xx(22)/(7)xx7xx7=308` sq cm

Total surface area of cylinder `=2πr(r+h)`

Total surface area of cylinder A `=2xx(22)/(7)xx7/2(7/22+14)`

`=22xx(35)/(2)=385` sq cm

Total surface area of cylinder B `=2xx(22)/(7)xx7xx(7+7)`

`=44xx14=616` sq cm

Question 3: Find the height of a cuboid whose base area is 180 cm² and volume is 900 cm³?

Answer: Volume = Base Area x Height

`text(Height)=text(Volume)/text(Base Area)`

`=(900)/(180)=5` cm

Question 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?

Answer: Number of cubes `=text(Volume of cuboid)/text(Volume of cubes)`

`=(60xx54xx30)/(6xx6xx6)`

`=10xx9xx5=450`

Question 5: Find the height of the cylinder whose volume is 1.54 m³ and diameter of the base is 140 cm?

Answer: Volume of cylinder `=πr^2h`

So, Height `=text(Volume)/(πr^2)`

`=(1.54)/((22)/(7)xx(70)/(100)xx(70)/(100))`

`=(1.54xx100)/(22xx7)=(154)/(154)=1` meter

Question 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?

Answer: Volume of milk tank `=πr^2h`

`=(22)/(7)xx1/5xx1/5xx7=49.5` cubic meter

As we know, 1 cubic metre = 1000 litres
So, 49.5 cubic metre = 49500 litres

Question 7: If each edge of a cube is doubled,

(i) how many times will its surface area increase?
Answer: Whenever sides are doubled in any structure then area becomes 4 times the original structure

(ii) how many times will its volume increase?
Answer: (ii) Volume becomes 8 times of the original volume if sides are doubled in any structure

Question 8: Water is pouring into a cubiodal reservoir at the rate of 60 litres per minute. If the volume of reservoir is 108 m³, find the number of hours it will take to fill the reservoir.

Answer: 108 cubic metre = 108000 litre
So, time = Volume ÷ Rate per minute

= 108000 ÷ 60 = 1800 min = 30 hour