RD Sharma Class 9 Solutions Chapter 19 Exercise 19.1 (Updated for 2023)

RD Sharma Class 9 Solutions Chapter 19 Exercise 19.1: This exercise deals with a surface area of a cylinder. Practice problems on surface areas of a circular cylinder through solved RD Sharma solutions to have a better understanding of the topic. The solutions that are provided here have been prepared by subject experts to further help students boost their scoring potential in the examination.

These solutions are created by the expert’s team. You can easily download RD Sharma Class 9 Solutions Chapter 19 Exercise 19.1 from the link provided in this article. 

• RD Sharma Class 9 Maths Solutions

Download RD Sharma Class 9 Solutions Chapter 19 Exercise 19.1

RD Sharma Class 9 Solutions Chapter 19 Exercise 19.1

Access RD Sharma Class 9 Solutions Chapter 19 Exercise 19.1

Question 1.
The curved surface area of a right circular cylinder is 4.4 m2. If the radius of the base of the cylinder is 0.7 m, find its height. [NCERT]
Solution:
The curved surface area of a cylinder = 4.4 m²
Radius (r) = 0.7 m

Question 2.
In a hot water heating system, there is a cylindrical pipe of length 28 m and diameter 5 cm. Find the total radiating surface in the system. [NCERT]
Solution:
Diameter of the pipe = 5 cm

Question 3.
A cylindrical pillar is 50 cm in diameter and 3.5 m in height. Find the cost of painting the curved surface of the pillar at the rate of 12.50 per m². [NCERT]
Solution:
The diameter of the cylindrical pillar = is 50 cm

Question 4.
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 is required for the same? [NCERT]
Solution:
Height of cylinder (h) = 1 m = 100 cm
Diameter of box = 140 cm

Question 5.
The total surface area of a hollow cylinder which is open from both sides is 4620 sq. cm, the area of the base ring is 115.5 sq. cm, and the height is 7 cm. Find the thickness of the cylinder.
Solution:
The total surface area of a hollow cylinder open from both sides = 4620 cm²
Area of base of ring = 115.5 cm²
Height (h) = 7 cm
Let outer radius (R) = R
and inner radius = r

Question 6.
Find the ratio between the total surface area of a cylinder to its curved surface area, given that its height and radius are 7.5 cm and 3.5 cm.
Solution:
The radius of the cylinder (r) = 3.5 cm
and height (h) = 7.5 cm
Total surface area = 2πr (h + r)
and curved surface area = 2πrh

Question 7.
A cylindrical vessel, without a lid, has to be tin-coated on both sides. If the radius of the base is 70 cm and its height is 1.4 m, calculate the cost of tin-coating at the rate of ₹3.50 per 1000 cm².
Solution:
The radius of the base of a cylindrical vessel (r) = 70 cm
and height (h) = 1.4 m = 140 cm
Total surface area (excluding upper lid) on both sides = 2πrh x 2 + πr² x 2

Question 8.
The inner diameter of a circular well is 3.5 m. It is 10 m deep. Find:
(i) inner curved surface area.
(ii) the cost of plastering this curved surface at the rate of ₹40 per m². [NCERT]
Solution:
The inner diameter of a well = 3.5 m

Question 9.
The students of a Vidyalaya were asked to participate s a competition for making and decorating pen holders in the shape of a cylinder with a base, using cardboard. Each pen holder was to be of radius 3 cm and height 10.5 cm. The Vidyalaya was to supply the competitors with cardboard. If there were 35 competitors, how much cardboard was required to be bought for the competition? [NCERT]

Solution:
The radius of cylindrical pen holder (r) = 3 cm
Height (h) = 10.5 cm
∴ The surface area of the pen holder

Question 10.
The diameter of the roller 1.5 m long is 84 cm. If it takes 100 revolutions to level a play¬ground, find the cost of leveling this ground at the rate of 50 paise per square meter.
Solution:

Diameter of a roller = 1.5 m
∴ Radius = 1.52 = 0.75 m = 75 cm
and length (h) = 84 cm

Question 11.
Twenty cylindrical pillars of the Parliament House are to be cleaned. If the diameter of each pillar is 0.50 m and the height is 4 m. What will be the cost of cleaning them at the rate of ₹2.50 per square meter? [NCERT]
Solution:

Number of pillars = 20
Diameter of one pillar = 0.50 m

Question 12.
A solid cylinder has a total surface area of 462 cm². Its curved surface area is one-third of its total surface area. Find the radius and height of the cylinder.
Solution:
The total surface of the solid cylinder = 462 cm²
Curved surface area = 13 of the total surface area

Question 13.
The total surface area of a hollow metal cylinder, open at both ends of an external radius of 8 cm and height of 10 cm is 338 π cm². Taking r to be the inner radius, obtain an equation in r and use it to obtain the thickness of the metal in the cylinder.
Solution:

The total surface area of a hollow metal cylinder = 338π cm²
Let R be the outer radius, r be the inner radius and h be the height of the cylinder the cylinder
∴ 2πRh + 2πrh + 2πR² – 2πr² = 338π
R = 8 cm, h = 10 cm
⇒ 2πh (R + r) + 2π(R² – r²) = 338π
⇒ Dividing by 2π , we get
⇒ h(R + r) + (R² – r²) = 169
⇒ 10(8 + r) + (8 + r) (8 – r) = 169
⇒ 80 + 10r + 64 – r² = 169
⇒ 10r – r² + 144 – 169 = 0
⇒ r² – 10r + 25 = 0
⇒ (r-5)² = 0
⇒ r = 5
∴ Thickness of the metal = R – r = 8 – 5 = 3 cm

Question 14.
Find the lateral curved surface area of a cylindrical petrol storage tank that is 4.2m in diameter and 4.5 m high. How much steel was actually used, if 112 of steel actually used was wasted in making the closed tank? [NCERT]
Solution:
Diameter of a cylindrical tank = 4.2 m

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