The total surface area of a square-based right pyramid is 1536 m2, of which 37.5% is the area of the base of the pyramid. What is the volume (in m3) of this pyramid?
Show answer & explanation
Correct answer: B
Explanation
The correct answer is option 2 i.e. 3072.
Given that
The total surface area of a square-based right pyramid is 1536 m2
The area of the base of the pyramid = 37.5% × Total surface area
Let the side of the square base be a
l2 = (side/2)2 + height2
where, l = slant height
The lateral surface area of the pyramid = 1/2 × Perimeter of the base × slant height
Total surface area of pyramid = Lateral surface area + Base area
Volume of pyramid = 1/3 × Base area × height
⇒ Base area = 37.5% × 1536 = (3/8) × 1536 = 576 cm2
⇒ a2 = 576
⇒ a = √576 = 24 cm
⇒ Lateral surface area = Total area - base area = 1536 - 576 = 960 cm2
⇒ 1/2 × 4a × l = 960
⇒ 2 × 24 l = 960
⇒ l = 20 cm
⇒ Now, l2 = (side/2)2 + height2
⇒ 202 = (24/2)2 + h2
⇒ h2 = 400 - 144 = 256
⇒ height = 16 cm
Hence, Volume of pyramid = 1/3 × 576 × 16 = 3072 cm3