Mensuration Exercise 15.1 – Questions:
- The height of a right circular cylinder is 14 cm and the radius of its base is 2 cm. Find its (i) CSA (ii) TSA
- An iron pipe 0 cm long has external radius equal to 12.5 cm and external radius equal to 11.5 cm. Find the TSA of the pipe.
- The radii of two circular cylinders are in the ratio 2:# and the ratio of their curved surface areas is 5:6. Find the ratio of their heights.
- The inner diameter of a circular well is 2.8 cm. It is 10 m deep. Find its inner curved surface area. Also find the cost of plastering this curved surface at the rate of Rs. 42 per m2?
- Craft teacher of the school taught the students to prepare cylindrical pen holders out of card board. In a class of strength 42, if each child prepared a pen holder of radius 5 cm and height 14 cm, how much cardboard was consumed?
- The diameter of a garden roller is 1.4 m and 2 m long. How much area will it cover in 5 revolutions?
- Find the volume of right circular cylinder whose radius is 10.5 cm and height is 16 cm.
- The inner diameter of a cylinder wooden pipe is 24 cm and its outer diameter is 28 cm. The pipe is 35 cm long. Find the mass of the pipe if 1cm3 of wood has a mass of 0.6 gm.
- Two circular cylinder of equal volumes have their heights in the ratio 1:2. Find the ratio of their radii.
- A rectangular sheet of paper, 44 cm x 20 cm is rolled along its length to form a cylinder. Find the volume of the cylinder so formed.
Mensuration Exercise 15.1 – Solutions:
- The height of a right circular cylinder is 14 cm and the radius of its base is 2 cm. Find its (i) CSA (ii) TSA
Solution:
Given:
Height of a right circular cylinder, h = 14 cm.
Radius = 2 cm
(i) CSA of cylinder = 2πrh
= 2 x 22/7 x 2 x 14
= 176 cm2
(ii) TSA of cylinder = 2πr(h + r)
= 2 x 22/7 x 2 x (14 + 2)
= 201.14 cm2
- An iron pipe 20 cm long has external radius equal to 12.5 cm and external radius equal to 11.5 cm. Find the TSA of the pipe.
Solution:
Given:
h = 20 cm
External radius = R = 12.5 cm
Inner radius = r = 11.5 cm
(a) Inner CSA = S1 = 2πrh = 2 x 22/7 x 11.5 x 20 = 1445.71 cm2
(b) Outer CSA = S2 = 2πRh = 2 x 22/7 x 12.5 x 20 = 1571.43 cm2
(c) TSA = S1 + S2 + area of two bases
= S1 + S2 + 2(πR2 – πr2)
= 1445.71 + 1571.43 + 2[22/7(12.5)2 – 22/7(11.5)2]
= 3167.98 cm2
- The radii of two circular cylinders are in the ratio 2:3 and the ratio of their curved surface areas is 5:6. Find the ratio of their heights.
Solution:
Let the radii of 2 cylinders be 2r and 3r respectively and their curved surface areas be 5cm2 and 6cm2 respectively.
We know, Curved surface area S = 2πrh
Then, h = S/2πr
Let h1 be the height of the cylinder of radii 2r and curved surface area 5 cm2 = 5/2πx2r = 5/4πr
Let h2 be the height of the cylinder of radii 3r and curved surface area 6 cm2 = 6/2πx3r = 1/πr
Therefore, h1/h2 = (5/4πr)/(1/πr) = 5/4
h1: h2 = 5: 4
- The inner diameter of a circular well is 2.8 cm. It is 10 m deep. Find its inner curved surface area. Also find the cost of plastering this curved surface at the rate of Rs. 42 per m2?
Solution:
Inner diameter of a circular well = 2.8 cm r = 2.8/2 = 1.4 cm and h = 10 m
Inner curved surface area = 2πrh = 2 x 22/7 x 1.4 x 10 = 88 cm2
The cost of plastering for curved surface area 1m2 is 42. Then, the cost of plastering 88cm2 =Rs. 3696
- Craft teacher of the school taught the students to prepare cylindrical pen holders out of card board. In a class of strength 42, if each child prepared a pen holder of radius 5 cm and height 14 cm, how much cardboard was consumed?
Solution:
No. of students = 42
radius of the pen holder, r = 5 cm
height of the pen holder, h = 14 cm
The card board consumed for 1 pen holder = curved surface area + area of the base = 2πrh + πr2
= 2 x 22/7 x 5 x 14 + 22/7 x 52
= 440 +78.57
= 518.57 cm2
Card board consumed to make 1 pen holder is 518.57cm2. Then the card board consumed to make 42 pen holder = 42×518.57 = 21780 cm2
- The diameter of a garden roller is 1.4 m and 2 m long. How much area will it cover in 5 revolutions?
Solution:
The diameter of the garden roller, d = 1.4 m
Then, radius, r = 1.4/2 = 0.7m
Height of the garden roller, h = 2m
Curved surface area = 2πrh
= 2 x 22/7 x 0.7 x 2
= 8.8 m2
No. of revolutions garden roller takes is 5. Then the area covered in 5 revolutions = 8.8 x 5 = 44m2
- Find the volume of right circular cylinder whose radius is 10.5 cm and height is 16 cm.
Solution:
Radius of the right circular cylinder, r = 10.5 cm
Height of the right circular cylinder, h = 16 cm
Volume of a cylinder = πr2h
= 22/7 x 10.52 x 16
= 5544 cm3
- The inner diameter of a cylinder wooden pipe is 24 cm and its outer diameter is 28 cm. The pipe is 35 cm long. Find the mass of the pipe if 1cm3 of wood has a mass of 0.6 gm.
Solution:
Inner diameter of a cylinder wooden pipe, d = 24 cm, r = 24/2 = 12 cm
Outer diameter of a cylinder wooden pipe, D = 28 cm, d = 28/2 = 14 cm
Height of a cylinder wooden pipe, h = 35 cm
Volume of the of a cylinder wooden pipe, V = πR2h – πr2h
= 22/7 x 35x(142 – 122)
= 5720 cm3
The mass of the pipe if 1cm3 of wood has a mass of 0.6 gm = 5720 x 0.6 = 3432 gm.
- Two circular cylinder of equal volumes have their heights in the ratio 1:2. Find the ratio of their radii.
Solution:
Ratio of heights of two circular cylinders of equal volumes = 1:2
Therefore, h1 = 1 and h2 = 2
Volume of the circular cylinder = πr2h
Given, V1 = V2 = V
Radius of the circular cylinder of h1 = 1, πr12h = V, r12 = V/πh1
Radius of the circular cylinder of h2 = 2, πr22h = V, r22 = V/πh2
Ratio of their radii = r12/r22 = (V/πh1)/ (V/πh2) = h2/h1 = 2/1
r1/r2 = √(2/1) = √2/1
Therefore, ratio of their radii = √2:1
- A rectangular sheet of paper, 44 cm x 20 cm is rolled along its length to form a cylinder. Find the volume of the cylinder so formed.
Solution:
Area of rectangular sheet = Curved surface area of the cylinder =
⇒ l x b = 2πr x h
⇒ 44cm x 20cm = l x b
Thus, h = 20 cm and 2πr = 44 cm
⇒ 2πr = 44 cm
⇒ πr = 22
⇒ r = 22×7/22 = 7 cm
Volume of the cylinder = πr2h
= 22/7 x 72 x 20
= 3080 cm3
