RD Sharma 2020 solution class 9 chapter 19 Surface Area and Volume of a Right Circular Cylinder Exercise 19.1

Exercise 19.1

Page-19.8

Question 1:

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.

Answer 1:

In the problem it is given that the Curved Surface Area of the cylinder is.

We know that,

Curved Surface Area of a cylinder

Where, radius of the cylinder and height of the cylinder

In the given problem, and h is to be found out.

Let us substitute all the given values in the formula for Curved Surface Area of the cylinder.

We have,

For simplifying the, this can be written as,

Now, clearly m

Therefore, the height of the cylinder is 1 meter.

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.

Answer 2:

The following data is given in the problem:

h = 28 m

Diameter = 5 cm

We are asked to find the Total radiating surface, which is nothing but the Total Surface Area of the cylinder.

The height of the cylinder is in meters, so let us first convert it into centimeters.

h = 2800 cm

Also, the diameter of the cylinder is given, but we want the radius.

The formula for finding out the Total Surface Area is:

Total Surface Area

Substituting the above values in this equation, we have

Total Surface Area

Total Surface Area

Total Surface Area

Therefore, the answer to this problem is

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.

Answer 3:

The data given in the problem is as follows:

Diameter of the cylinder =50cm

Height = 3.5m

Painting charges = Rs.12.50 per m²

We have to find the total cost of painting the pillar

To find the cost of painting the pillar, we should first find the Curved Surface Area of the pillar using the given data.

Curved Surface Area

r =

Since the painting charges are given in terms of, we shall convert the radius from centimeters to meters.

r = 0.25m

Substituting the values in the formula for Curved Surface Area, we have

Curved Surface Area

Curved Surface Area = 5.5 m²

It is given that, for 1 m² the cost of painting is Rs.12.50

Therefore,

Total cost of painting the pillar =

= 68.75

Therefore, the answer to this questions is, Rs.68.75

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 metres of the sheet are required for the same?

Answer 4:

The data given in the problem is as follows:

h = 1 m

Diameter = 140 cm

We are asked to find the area of the sheet in square meters required to make this cylinder.

Since it is a closed cylinder, the area of the sheet required to make this will be equal to the Total surface area of the cylinder.

Total surface area

= =70cm

Since area is asked in square meters, let us convert the radius from centimeters to meters.

r = 0.7m

Substituting the values in the formula for the Total Surface Area of a cylinder, we have

Total Surface Area

Total Surface Area = 7.48

Therefore, the area of sheet required to make this cylinder is 7.48 square meters.

Question 5:

The total surface area of a hollow cylinder which is open from both sides is 4620 sq. cm, area of base ring is 115.5 sq. cm and height 7 cm. Find the thickness of the cylinder.

Answer 5:

Data given is the problem is as follows:

The cylinder is a hollow cylinder and is open on both sides

Total surface area of the cylinder is 4620 square centimeters

Area of the base ring = 115.5 square centimeters

Height = 7 cm

We are supposed to find the thickness of this cylinder.

We know that,

Total surface area of a hollow cylinder

Where, r is the inner radius and R is the outer radius of the cylinder.

Now we have,

= 4620

Also, h = 7cm

= 4620

Also, it is given that

Area of base ring = 115.5

That is, = 115.5 …..(1)

Substituting for in the above equation, we have

2(115.5) = 4620

=4389

Also, h = 7

Therefore,

.….(2)

Now let us again take up equation (1)

= 115.5

From equation (2) we have . Substitute this in the above equation.

(R – r) is nothing but the thickness of the cylinder.

Therefore, the thickness of the cylinder is cm

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.

Answer 6:

Data given in the problem is as follows:

h =7.5 cm

r = 3.5 cm

We are supposed to find the ratio between the Total Surface Area and the Curved Surface Area.

We know that,

Total Surface Area (TSA) =

Curved Surface Area (CSA) =

Therefore,

=

=

Substituting the values of h and r in the above expression, we have

=

= ==

Hence the ratio between Total Surface area and Curved Surface Area is 22 : 15.

Question 7:

A cylindrical vessel, without lid, has to be tin-coated on its 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 Rs 3.50 per 1000 cm².

Answer 7:

It is given that,

r = 70 cm

h = 1.4 m

Tin coating rate = cm²

We have to find the total cost of coating the cylinder with tin.

Let us first convert h from meters to centimeters.

h = 1.4 m

= 140 cm

Since the cylindrical vessel without lid has to be coated both on the inner side as well the outer side,

Area to be coated =

=

= 154000 cm²

Now let us find the total cost of coating this area.

For 1000 cm² the cost of coating is Rs.3.50

For 154000 cm² the cost of coating is given by =539

Therefore the total cost of coating the vessel on both inner and outer sides is Rs.539

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 Rs 40 per m².

Answer 8:

Given data is as follows:

Inner diameter of the well = 3.5 m

h = 10 m

Rate of plastering = Rs.40 per square meter

We have to find two things,

1. Inner curved surface area

2. Total cost of plastering the inner curved surface

(i)

Inner curved surface area = 110

(ii) Now, let us find the total cost of plastering this area.

It is given that for 1the cost of plastering is Rs.40

Therefore, for 110 the cost of plastering =

= 4400

Cost of plastering = Rs 4400

Question 9:

The students of a Vidyalaya were asked to participate in 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 carboard. If there were 35 competitors, how much cardboard was required to be bought for the competition?

Answer 9:

Question 10:

The diameter of roller 1.5 m long is 84 cm. If it takes 100 revolutions to level a playground, find the cost of levelling this ground at the rate of 50 paise per square metre.

Answer 10:

Given that height h = 1.5 m
Diameter = 84 cm = 0.84 m
Radius = $\frac{0.84}{2}=0.42 \mathrm{m}$

Now, we have to find the area of the ground.

= 396 m²

Cost of leveling for 1 m² = 0.50

Cost of leveling for 396 m² = ​

Cost of leveling for 396 m² = Rs.198

Question 11:

Twenty cylindrical pillars of the Parliament House are to be cleaned. If the diameter of each pillar is 0.50 m and height is 4 m. What will be the cost of cleaning them at the rate of Rs 2.50 per square metre?

Answer 11:

Total cost of cleaning = Rs.314.28

Question 12:

A solid cylinder has 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.

Answer 12:

The data given in this problem is as follows:

Total Surface Area of the cylinder = 462 cm²

Curved Surface Area (CSA) = Total Surface Area (TSA)

We have to find the radius and the height of the cylinder.
 

Using the given data, we have

Substituting the formula for Curved Surface Area and Total Surface Area in the above equation, we have

=

=

We have,

Total Surface Area = 462 cm²

Substituting the formula for Total Surface Area in the above equation, we get

= 462

= 462

Now, we know that

Substituting this in the above equation, we have

Since

Therefore, the final answer to this question is,

Radius of the cylinder = 7cm

Height of the cylinder = 3.5cm

Question 13:

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

Answer 13:

Data given in the problem is as follows:

Given cylinder is a hollow cylinder

External radius (R) = 8cm

Height (h) = 10cm

Total Surface Area = 338π

We have to obtain an equation in r, where r is the inner radius of the cylinder and using this equation we have to find the thickness of the cylinder.

We know that,

Total Surface Area of a hollow cylinder =

Therefore,

=

= 338

Thickness  = R – r = 8 – 5 = 3 cm

Thickness of the cylinder is 3 cm

Page-19.9

Question 14:

Find the lateral curved surface area of a cylinderical petrol storage tank that is 4.2 m in diameter and 4.5 m high. How much steel was actually used, if $\frac{1}{12}$of steel actually used was wasted in making the closed tank?

Answer 14:

Actual area of steel used = 95.04 m²