Find the total surface area of a right circular cylinder whose radius is 6 cm and height 15 cm. Use $π = \frac{22}{7}$ .

medium 2 marks Class 6 · Mathematics · Mensuration

Answer

792 cm

^{2}

The correct answer is 792 cm $^{2}$ — Therefore the total surface area is $792$ square centimetres.

Step-by-step solution

Recall the surface area formula: $S = 2 p i r^{2} + 2 p i r h$ for a right circular cylinder.
Compute the base area term: $2 π r^{2} = 2 \times \frac{22}{7} \times 6^{2} = 2 \times \frac{22}{7} \times 36 = \frac{1584}{7}$ .
Compute the lateral area term: $2 π r h = 2 \times \frac{22}{7} \times 6 \times 15 = 2 \times \frac{22}{7} \times 90 = \frac{3960}{7}$ .
Add the two terms: $\frac{1584}{7} + \frac{3960}{7} = \frac{5544}{7}$ .
Convert the fraction to a whole number: $\frac{5544}{7} = 792$ .
Therefore the total surface area is $792$ square centimetres.

Common mistake: Adding the height instead of multiplying it with

2 p i r

Concept tested: Surface area of cylinder