A solid right circular cylinder has radius 5 cm and height 12 cm. Find its total surface area. Use π = 22/7 and give the answer in square centimetres, correct to the nearest integer.

A solid right circular cylinder has radius $5 cm$ and height $12 cm$ . Find its total surface area. Use $π = \frac{22}{7}$ and give the answer in square centimetres, correct to the nearest integer.

medium 2 marks Class 10 · Mathematics · Surface Areas and Volumes

Answer

534 cm^{2}

The correct answer is $534 cm^{2}$ — Round to the nearest integer: $534$ cm $^{2}$ .

Total surface area of a cylinder = $2 π r (r + h)$ .
Substitute $r = 5$ , $h = 12$ : $2 π \times 5 \times (5 + 12) = 10 π \times 17$ .
Calculate $10 \times 17 = 170$ , so area = $170 π$ cm $^{2}$ .
Replace $π$ by $22/7$ : $170 \times \frac{22}{7} = \frac{3740}{7}$ .
Divide: $3740 \div 7 = 534.2857 \dots$ .
Round to the nearest integer: $534$ cm $^{2}$ .

Common mistake: Using

π r^{2} h

instead of

2 π r (r + h)

for total surface area

Concept tested: Total surface area of a cylinder