Question

In the following table information about a few cylinders are given, copy and complete the table.

	Radius(cm)	Height(cm)	Curved surface	Area of base	Total surface
i)	7	9
ii)	14	10
iii)	21	5

Answer 1

Hint: In this problem we will use the following formulas to find the curved surface area, area of base and total surface for different radius and height.
Curved surface area of cylinder$ = 2\pi rh$
Base area of cylinder$ = \pi {r^2}$
Total surface area of cylinder$ = 2\pi r\left( {r + h} \right)$

Complete step-by-step answer:
We have given the radius of cylinder which are 7, 14, and 21 in cm and height of cylinder are 9, 10, and 5 in cm.
First, we will solve for the cylinder having radius 7cm and height 9cm.
Curved surface area of this cylinder is given using the formula:
Curved surface area of this cylinder$ = 2\pi rh$.
Now, substitute the values of radius and height in the formula of the curved surface area of the cylinder.
Curved surface area of this cylinder $ = 2 \times \pi \times 7 \times 9$
Curved surface area of this cylinder $ = 396{\text{ }}c{m^2}$
So, the curved surface area of the cylinder is $396{\text{ }}c{m^2}$.
Now, we will find the area of the base of the cylinder which is equal to $\pi {r^2}$.
Now, substitute the values of radius and height in the formula of surface area of the base of the cylinder.
Surface area of base of cylinder $ = \pi \times {\left( 7 \right)^2}$
Surface area of base of cylinder $ = 154{\text{ }}c{m^2}$
So, the area of base is $154{\text{ }}c{m^2}$ .
Now we will find the total surface area which is equal to $2\pi r\left( {r + h} \right)$.
Now substitute the values of radius and height of the cylinder in the formula of total surface of cylinder.
Total surface area$ = 2 \times \pi \times 7 \times \left( {7 + 9} \right)$
Total surface area$ = 2 \times 3.14 \times 7 \times \left( {16} \right)$
Total surface area$ = 704{\text{ }}c{m^2}$
So, the total surface area of the cylinder having radius 7cm and height 9cm is $704{\text{ }}c{m^2}$ .
Now, we will solve for the cylinder having radius 14cm and height 10cm.
First, we will find the curved surface area of the cylinder which is $2\pi rh$.
Now, substitute the values of radius and height of the cylinder in the formula of curved surface area of the cylinder.
Curved surface area of cylinder $ = 2 \times \pi \times 14 \times 10$
Curved surface area of cylinder $ = 880{\text{ }}c{m^2}$
So, the curved surface area of the cylinder is $880{\text{ }}c{m^2}$ .
Now, we will find the area of base which equal to $\pi {r^2}$
Now, substitute the values of radius and height in the formula of area of base.
Area of base$ = \pi \times {\left( {14} \right)^2}$
Area of base$ = 616{\text{ }}c{m^2}$
So, the area of the base of the cylinder having radius 14cm and height 10cm is $616{\text{ }}c{m^2}$ .
Now, we will find the total surface area of the cylinder which is $2\pi r\left( {r + h} \right)$
Now, substitute the values of radius and height in the formula of total surface area of the cylinder.
Total surface area of the cylinder \[ = 2 \times \pi \times 14 \times \left( {14 + 10} \right)\]
Total surface area of the cylinder \[ = 2 \times 3.14 \times 14 \times \left( {24} \right)\]
Total surface area of the cylinder \[ = 2112{\text{ }}c{m^2}\]
So, the total surface area of the cylinder having radius 14cm and height 10cm is $2112{\text{ }}c{m^2}$ .
Now, we will solve for the cylinder having radius 21cm and height 5cm.
First we will find the curved surface area of the cylinder which is $2\pi rh$.
Now, substitute the values of radius and height of the cylinder in the formula of curved surface area of the cylinder.
Curved surface area of cylinder $ = 2 \times \pi \times 21 \times 5$
Curved surface area of cylinder $ = 660{\text{ }}c{m^2}$
So, the curved surface area of the cylinder is $660{\text{ }}c{m^2}$.
Now, we will find the area of the base which is equal to $\pi {r^2}$.
Now, substitute the values of radius and height in the formula of area of base.
Area of base$ = \pi \times {\left( {21} \right)^2}$
Area of base$ = 1386{\text{ }}c{m^2}$
So, the area of the base of the cylinder having radius 14cm and height 10cm is ${\text{1386 }}c{m^2}$ .
Now, we will find the total surface area of the cylinder which is $2\pi r\left( {r + h} \right)$
Now, substitute the values of radius and height in the formula of total surface area of the cylinder.
Total surface area of cylinder\[ = 2 \times \pi \times 21 \times \left( {21 + 5} \right)\]
Total surface area of cylinder\[ = 2 \times 3.14 \times 21 \times \left( {26} \right)\]
Total surface area of cylinder\[ = 3432{\text{ }}c{m^2}\]
So, the total surface area of cylinder having radius 21cm and height 5cm is ${\text{3432 }}c{m^2}$
So, the required table will be,

	Radius(cm)	Height(cm)	Curved surface(in $c{m^2}$)	Area of base(in $c{m^2}$)	Total surface(in $c{m^2}$)
i)	7	9	396	154	704
ii)	14	10	380	616	2112
iii)	21	5	660	1386	3432

Note: The curved surface area of the cylinder is the area of the curved part of the cylinder, and it is also called the Lateral Surface area of the cylinder.
The total surface area of the cylinder is the sum of the curved surface area of the cylinder and the area of the base and top of the cylinder.