EXERCISE 13.2
Assume re = 22, unless stated otherwise,
The curved surface area of a right circular cylinder of height 14 cm is 88 cm². Find the
diameter of the base of the cylinder.
It is required to make a closed cylindrical tank of height 1 m and base diameter 140 cm
from a metal sheet. How many square metres of the sheet are required for the same?
A metal pipe is 77 cm long. The inner diameter of a cross
section is 4 cm, the outer diameter being 4.4 cm
(see Fig. 13.11). Find its
6) inner curved surface area,
(ii) outer curved surface area,
(iii) total surface area.
Answers
Answer:
Assume unless stated otherwise
1. The curved surface area of a right circular cylinder of height 14 cm is 88 cm2. Find the diameter of the base of the cylinder.
Ans. Given: Height of cylinder = 14 cm, Curved Surface Area = 88 cm2
Let radius of base of right circular cylinder = cm
= 88
1 cm
Diameter of the base of the cylinder = = 2 x 1 = 2 cm
2. It is required to make a closed cylindrical tank of height 1 m and base diameter 140 cm from a metal sheet. How many square meters of the sheet are required for the same?
Ans. Given: Diameter = 140 cm
Radius = 70 cm = 0.7 m
Height of the cylinder = 1 m
Total Surface Area of the cylinder
=
=
= 2 x 22 x 0.1 x 1.7 = 7.48 m2
Hence 7.48 m2 metal sheet is required to make the close cylindrical tank.
3. A metal pipe is 77 cm long. The inner diameter of a cross section is 4 cm, the outer diameter being 4.4 cm. [See fig.]. Find its:
(i) Inner curved surface area
(ii) Outer curved surface area
(iii) Total surface area
Ans. (i) Length of the pipe = 77 cm, Inner diameter of cross-section = 4 cm
Inner radius of cross-section = 2 cm
Inner curved surface area of pipe = =
= 2 x 22 x 2 x 11 = 968 cm2
(ii) Length of pipe = 77 cm, Outer diameter of pipe = 4.4 cm
Outer radius of the pipe = 2.2 cm
Outer surface area of the pipe =
=
= 44 x 2.2 x 11 = 1064.8 cm2
(iii) Now there are two circles of radii 2 cm and 2.2 cm at both the ends of the pipe.
Area of two edges of the pipe = 2 (Area of outer circle – area of inner circle)
= =
= =
= = 5.28 cm2
Total surface area of pipe
= Inner curved surface area + Outer curved surface area + Area of two edges
= 968 + 1064.8 + 5.28 = 2038.08 cm2
Step-by-step explanation:
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Answer:
Let the radius and height of the cylinder be 'r' and 'h' respectively.
Curved Surface Area of a right circular cylinder = 2 π r h
Diameter = 2 × radius
Height of the cylinder, h = 14 cm
CSA of the cylinder = 88 cm²
2 π r h = 88 cm²
2 × 22/7 × r × 14 cm = 88 cm²
r = (88 cm² × 7) / (2 × 22 × 14) cm
= 1 cm
Diameter = 2 × radius
= 2 × 1 cm
= 2 cm
Thus, the diameter of the base of the cylinder is 2 cm.
Step-by-step explanation:
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