Subject: General Aptitude · Chapter: Volume and Surface Area · Exam: · Marks: · Difficulty:
A right pyramid has an equilateral triangular base of side 4 units. If the number of square units of its whole surface area is three times the number of cubic units of its volume, find its height.
(a)3 units
(b)4 units
(c)5 units
(d)6 units
Answer
Answer (as printed): B
Explanation
Let the height of the pyramid be $h$ units. Then, volume of the pyramid $$=\left[\frac{1}{3} \times\left(\frac{\sqrt{3}}{4} \times 4 \times 4\right) \times h\right] \text { cu. units }=\left(\frac{4 h}{\sqrt{3}}\right) \text { cu. units. }$$ Whole surface area of the pyramid $$\begin{aligned} & =\left[4 \times\left(\frac{\sqrt{3}}{4} \times 4 \times 4\right)\right] \text { sq. units. }=(16 \sqrt{3}) \text { sq. units } \\ & \therefore 16 \sqrt{3}=3 \times\left(\frac{4 h}{\sqrt{3}}\right) \Rightarrow h=4 \text { units. } \end{aligned}$$
Explanation as extracted from the printed page; notation may be imperfect.