Question
Download Solution PDFA square pyramid with side 10 cm has a volume of 400 cm3. Find the total surface area of the pyramid.
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFBase area of the pyramid = Area of square = (10)2 = 100 cm2
∵ Volume of pyramid = 1/3 × Base area × Height
⇒ 400 = 1/3 × 100 × Height
⇒ Height of pyramid (h)= 12 cm
Now,
⇒ Slant height of pyramid = √[(height)2 + (side/2)2] = √(144 + 25) = √169 = 13 cm
⇒ Area of a triangular face = 1/2 × side × slant height = 1/2 × 10 × 13 = 65 cm2
∵ A square pyramid has four triangular faces & a square base,
∴ Total surface area of pyramid = 4(65) + 100 = 360 cm2Last updated on Jun 13, 2025
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