(i) radius of the base = 7 cm and height = 50 cm (ii) radius of the base = 5.6 m and height = 1.25 m

Question

Find the volume, curved surface area and total surface area of each of the cylinders whose dimensions are: 

(i) radius of the base = 7 cm and height = 50 cm 

(ii) radius of the base = 5.6 m and height = 1.25 m 

(iii) radius of the base = 14 dm and height = 15 m

Answer 1

(i) At first, 

In order to find volume, we will use the following formula:

Volume of a cylinder = \(\pi r^2h\)

Where, 

‘r’ = radius of the base 

‘h’ = height of the cylinder 

Hence,

Volume of the cylinder = \(\pi\)(7)²(50)

= \(\frac{22}{7}\times7\times7\times50\)

= 22 × 7 × 50

= 7700 cm³

Now,

In order to find curved surface area, we will use the following formula:

Curved surface area of cylinder = \(2\pi rh\)

Where, 

‘r’ = radius of the base 

‘h’ = height of the cylinder 

Hence, 

Curved surface area of cylinder

r = \(2\pi rh\)

= \(2\times\frac{22}{7}\times7\times50\)

= 22 × 2 × 50 

= 2200 cm²

Now, 

In order to find the total surface area we will use the following formula: 

Total surface area of cylinder = \(2\pi r(r+h)\)

= \(2\times\frac{22}{7}\times7(7+50)\)

= 22× 2× 57 

= 2508cm²

(ii) At first, 

In order to find volume we will use the following formula: 

Volume of a cylinder = \(\pi r^2h\)

Where, 

‘r’ = radius of the base 

‘h’ = height of the cylinder 

Hence, 

Volume of the cylinder = \(\pi(5.6)^2(1.25)\)

= \(\frac{22}{7}\times5.6\times5.6\times1.25\)

= 22 × 0.8 × 7 × 50 

= 123.2 cm³ 

Now, 

In order to find curved surface area we will use the following formula: 

Curved surface area of cylinder = \(2\pi rh\)

Where, 

‘r’ = radius of the base 

‘h’ = height of the cylinder 

Hence, 

Curved surface area of cylinder = \(2\pi rh\)

= \(2\times\frac{22}{7}\times5.6\times1.25\)

= 22 × 2 × 0.8 × 1.25

= 44 cm² 

Now, 

In order to find the total surface area we will use the following formula: 

Total surface area of cylinder = \(2\pi r(r+h)\)

Where, 

‘r’ = radius of the base 

‘h’ = height of the cylinder 

Hence, 

Total surface area of cylinder = \(2\pi r(r+h)\)

= \(2\times\frac{22}{7}\times5.6(5.6+1.25)\)

= 22 × 2 × 0.8 × 6.85 

= 241.12 cm²

(iii) At first, 

We will convert the radius into metre 

Radius = 14dm = 1.4m 

Now, 

In order to find volume we will use the following formula:

Volume of a cylinder = \(\pi r^2h\)

Where,

r’ = radius of the base 

‘h’ = height of the cylinder Hence, 

Volume of the cylinder = \(\pi (7)^2(50)\)

= \(\frac{22}{7}\times1.4\times1.4\times15\)

= 22 × 0.2 × 1.4× 1.5 

= 92.4cm³

Now, 

In order to find curved surface area we will use the following formula:

Curved surface area of cylinder = \(2\pi rh\)

Where, 

‘r’ = radius of the base 

‘h’ = height of the cylinder 

Hence, 

Curved surface area of cylinder = \(2\pi rh\)

= \(2\times\frac{22}{7}\times1.4\times1.5\)

= 22 × 2 × 0.2 × 1.5

= 132cm²

Now, 

In order to find the total surface area we will use the following formula: 

Total surface area of cylinder = \(2 \pi r(r+h)\)

Where, 

‘r’ = radius of the base 

‘h’ = height of the cylinder 

Hence, 

Total surface area of cylinder = \(2 \pi r(r+h)\)

= \(2\times\frac{22}{7}\times1.4(1.4+1.5)\)

= 22 × 2 × 0.2 × 2.9

= 144.32cm²