The base of a right pyramid is an equilateral triangle with side 10 cm, and its vertical height is 24 cm. Find the volume (in cm³) of the pyramid.

एक समकोण पिरामिड का आधार 10 सेमी भुजा वाला समबाहु त्रिभुज है तथा उसकी ऊँचाई 24 सेमी है। पिरामिड का आयतन (सेमी³ में) ज्ञात कीजिए।

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SSC, CGL MAINS 2026
  • A. 200√3 cm³
  • B. 100/3 cm³
  • C. 400√3 cm³
  • D. 150/3 cm³
Correct Answer :A - 200√3 cm³
Detailed Solution Video
Video Credit –Nikhil Sharma Maths
Detailed Text Solution

Volume of a pyramid = (1/3) × Base area × Height.

Base is an equilateral triangle of side 10 cm.

Area of equilateral triangle = (√3/4) × a²
= (√3/4) × 10²
= (√3/4) × 100
= 25√3 cm².

Height of pyramid = 24 cm.

Volume = (1/3) × 25√3 × 24
= 25√3 × 8
= 200√3 cm³.

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