Question

The volume of a cylinder of height 28 cm is 4312 cm . Find the surface area of the cylinder

Answer 1

Answer:

Let h be the height of cylinder.

Given that r= radius= 5 cm

Total surface area=165

Answer 2

The total surface area of cylinder is 1540 cm².

Given: A cylinder

• Height (h)=28 cm
• Volume (V)=4312 cm³

To find:

• Surface area of cylinder.

Solution:

Formula to be used:

1. Volume of cylinder: πr²h unit³
2. CSA of cylinder : 2πrh unit²
3. TSA of cylinder: 2πr(r+h) unit²

Step 1:

Calculate radius of cylinder using volume and it's formula.

$\pi {r}^{2} h = 4312$

or

$\frac{22}{7} \times {r}^{2} \times 28 = 4312$

or

$22 \times {r}^{2} \times 4= 4312$

or

${r}^{2} = \frac{4312}{22 \times 4}$

or

${r}^{2} = 49$

or

$\bf r = 7 \: cm$

Step 2:

Find CSA of cylinder.

$CSA = 2\pi \: rh$

$CSA = 2 \times \frac{22}{7} \times 7 \times 28$

or

$CSA = 44 \times 28$

or

$\bf CSA = 1232 \: {cm}^{2}$

Step 3:

Calculate TSA of cylinder.

$TSA = 2\pi \: r(r + h)$

or

$TSA = 2 \times \frac{22}{7} \times 7 \: (7 + 28)$

or

$TSA = 44(35)$

or

$\bf TSA = 1540 \: {cm}^{2}$

Thus,

Total surface area of cylinder is 1540 cm².

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