A regular rights pyramid has a square base with a side length of 12 cm. Its slant height is 8 cm. what is its volume?
A regular rights pyramid has a square base with a side length of 12 cm. Its slant height is 8 cm. what is its volume?
एक समलंब पिरामिड का आधार वर्गाकार है और इसकी भुजा की लंबाई 12सेमी है। इसकी तिर्यक ऊँचाई 8 सेमी है। इसका आयतन क्या है?
Detailed Solution & Logic
Correct Answer:
254 \(cm^3\)
Side of square base a = 12 cm
Slant height l = 8 cm
First find the vertical height hhh.
$l^2 = h^2 + \left(\frac{a}{2}\right)^2$
$8^2 = h^2 + 6^2$
$64 = h^2 + 36$
$h^2 = 28$
$h = \sqrt{28} = 2\sqrt{7}$
Volume of pyramid:
$V = \frac{1}{3} \times a^2 \times h$
$V = \frac{1}{3} \times 12^2 \times 2\sqrt{7}$
$V = 96\sqrt{7}$
$96\sqrt{7} \approx 96 \times 2.6458$
$V \approx 254 , cm^3$
Answer: 254 $ cm^3$
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