The volume of a solid cylinder is 5852 cm³ and its height is 38 cm. What is the total surface area of the solid cylinder? (Round your answer to the nearest integer)
(Use \(\pi\) = \(\frac{22}{7}\))

Question

Question

This question was previously asked in

RRB NTPC Graduate Level CBT-I Official Paper (Held On: 06 Jun, 2025 Shift 2)

Answer 1

Given:

Volume of cylinder (V) = 5852 cm³

Height of cylinder (h) = 38 cm

Value of \(\pi = \frac{22}{7}\)

Formula used:

Volume of a cylinder = \(\pi r^2 h\)

Total Surface Area of a solid cylinder = \(2\pi r(r + h)\)

Where r = radius

Calculations:

First, find the radius (r) using the volume formula:

V = \(\pi r^2 h\)

5852 = \(\frac{22}{7} \times r^2 \times 38\)

⇒ r² = \(\frac{5852 \times 7}{22 \times 38}\)

⇒ r² = \(\frac{40964}{836}\)

⇒ r² = 49

⇒ r = \(\sqrt{49}\)

⇒ r = 7 cm

Now, calculate the Total Surface Area (TSA) of the cylinder:

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

⇒ TSA = \(2 \times \frac{22}{7} \times 7 \times (7 + 38)\)

⇒ TSA = \(2 \times 22 \times 45\)

⇒ TSA = \(44 \times 45\)

⇒ TSA = 1980 cm²

∴ The total surface area of the solid cylinder is 1980 cm².