The circumference of the base of a conical tent of height 8 m is 32π m. Find its curved surface area.

Question

Accepted Answer

Step 1: Given circumference of base = 32π m.

Circumference of base of cone = 2πr  
=> 2πr = 32π  
=> r = 16 m

Step 2: Height (h) = 8 m

Step 3: Calculate slant height (l) using Pythagoras theorem:

l = √(r² + h²) = √(16² + 8²) = √(256 + 64) = √320 = √(64 × 5) = 8√5 m

Step 4: Curved surface area (CSA) of cone = πrl

= π × 16 × 8√5 = 128√5 π m²

Step 5: Check options:

Option 4 is 128√5 π m² which matches the calculated CSA.

Final answer: 128√5 π m².

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