Chapter 11: Mensuration

Yes, we can say that volume of cylinder B is greater, since radius of cylinder B is greater than that of cylinder A.

Find Volume for cylinders A and B

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

Find the surface area of cylinders A and B

Surface area of cylinder A =  2πr(r+h )

= 2 x 22/7 x 7/2 x (7/2 + 14) = 385

Surface area of cylinder A is385 cm²

Surface area of cylinder B =  2πr(r+h)

= 2×(22/7)×7(7+7) = 616

Surface area of cylinder B is 616 cm²

Yes, the cylinder with greater volume also has a greater surface area.

Given, Base area of cuboid = 180 cm² and Volume of cuboid = 900 cm³

We know that, Volume of cuboid = lbh

900 = 180×h (substituting the values)

h= 900/180 = 5

Hence the height of the cuboid is 5 cm.

Given, Length of cuboid, l = 60 cm, Breadth of cuboid, b = 54 cm and

Height of cuboid, h = 30 cm

We know that, Volume of cuboid = lbh = 60 ×54×30  = 97200 cm³

And Volume of cube = (Side)³

= 6×6×6 = 216 cm³

Also, the Number of small cubes =  volume of cuboid / volume of cube

= 97200/216

= 450

Hence , the required number of cubes is 450.

Given: Volume of cylinder = 1.54 m³and Diameter of cylinder = 140 cm

Radius  ( r )=  d/2 = 140/2  = 70 cm

Volume of cylinder = πr²h

1.54 = (22/7)×0.7×0.7×h

After simplifying, we get the value of h, which is,

h = (1.54×7)/(22×0.7×0.7)

h = 1

Hence, the height of the cylinder is 1 m.

Given, Radius of cylindrical tank, r = 1.5 m and 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

Hence, the required quantity of milk is 49500 litres.

(i) Let the edge of the cube be “ l” .

Formula for Surface area of the cube, A =  6 l²

When the edge of the cube is doubled, then

Surface area of the cube, say A’ = 6(2l)² = 6×4l² = 4(6 l²)

A’ = 4A

Hence, the surface area will increase by four times.

(ii) Volume of a cube, V = l³

When the edge of the cube is doubled, then

Volume of the cube, say V’ = (2l)³ = 8( l³)

V’ = 8×V

Hence, the volume will increase 8 times.

Given, the volume of the reservoir = 108 m³

Rate of pouring water into cuboidal reservoir = 60 litres/minute

=  60/1000  m³ per minute

Since 1 liter = (1/1000 )m³

=  (60×60)/1000 m³ per hour

Therefore, (60×60)/1000 m³ water filled in reservoir will take = 1 hour

Therefore 1 m³ water filled in reservoir will take =  1000/(60×60)  hours

Therefore, 108 m³ water filled in reservoir will take = (108×1000)/(60×60)  hours = 30 hours

Answer: It will take 30 hours to fill the reservoir.