Find the total surface area of a right circular cylinder whose radius is 3 cm and height is 12 cm.

hard 4 marks Class 7 · Mathematics · Visualising Solid Shapes

Answer

90\pi

The correct answer is 90\pi — Hence the surface area is $90 π$ cm², approximately $282.74$ cm².

Step-by-step solution

The total surface area of a cylinder is $2 π r (r + h)$ , where $r$ is radius and $h$ is height.
Substitute $r = 3$ cm and $h = 12$ cm: $2 π \times 3 \times (3 + 12)$ .
Simplify inside the parentheses: $3 + 12 = 15$ .
Compute the product: $2 π \times 3 \times 15 = 6 π \times 15 = 90 π$ .
Hence the surface area is $90 π$ cm², approximately $282.74$ cm².

Common mistake: Forgetting to add radius and height or using only one of them

Concept tested: Cylinder surface area formula