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Mensuration

Cylinder

EN हिंदी

✕

NTPC Graduate Tier 1 2025 Shift-3 📅 06 Jun, 2025

The curved surface area of a cylinder is half of its total surface area. If the height is 128 cm, then find the radius (in cm).

A

128

B

138

C

122

D

137

Result Summary

APEDIA

NTPC Graduate Tier 1

2025 • 06 Jun, 2025 • Shift-3

The curved surface area of a cylinder is half of its total surface area. If the height is 128 cm, then find the radius (in cm).

Correct Answer

128

Recalling Geometric Formulas: For a cylinder with radius 'r' and height 'h', the Curved Surface Area (CSA) is $2\pi rh$ and the Total Surface Area (TSA) is $2\p......

💡 Analysis & Explanation

Recalling Geometric Formulas ▼

For a cylinder with radius 'r' and height 'h', the Curved Surface Area (CSA) is $2\pi rh$ and the Total Surface Area (TSA) is $2\pi r(r + h)$.

Translating the Condition ▼

The problem states that CSA = $\frac{1}{2}$ * TSA. Substituting the formulas gives $2\pi rh = \frac{1}{2} \times 2\pi r(r + h)$.

Simplifying the Equation ▼

We can cancel $2\pi r$ from both sides of the equation (assuming $r$ is not zero). This leaves $h = \frac{1}{2}(r + h)$, which simplifies to $2h = r + h$. Subtracting 'h' from both sides yields $h = r$.

Final Calculation ▼

The problem provides the height $h = 128$ cm. Since we derived that the radius 'r' is equal to the height 'h', the radius must also be 128 cm.

Conclusion ▼

The radius of the cylinder is exactly 128 cm.