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 PDFGiven:
A square pyramid with side 10 cm has a volume of 400 cm3
Formula used:
Volume of pyramid = 1/3 × Base area × Height
Total surface area = base area + lateral surface area of square pyramid
Lateral surface area = 1/2 × perimeter of base × slant height
Calculation:
Base 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 = 12 cm
⇒ Slant height of pyramid = √[(height)2 + (side/2)2]
⇒√(144 + 25) = √169 = 13 cm
Lateral surface area = 1/2 × 4 × 10 × 13 = 260 cm2
Total surface area = 100 cm2 + 260 cm2 = 360 cm2
∴ the correct answer is 360 cm2.
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