Question : A prism has a regular hexagonal base with a side of 6 cm. If the total surface area of the prism is 216$\sqrt3$ cm2, then what is the height (in cm) of the prism?
Option 1: $3\sqrt3$
Option 2: $6\sqrt3$
Option 3: $6$
Option 4: $3$
Latest: SSC CGL preparation tips to crack the exam
Don't Miss: SSC CGL complete guide
Correct Answer: $3\sqrt3$
Solution :
Given: Side, $a$ = 6 cm
Let the height be $h$.
Area of the base of the hexagonal prism $=6 \times \frac{\sqrt3}{4}a^2=6 \times \frac{\sqrt3}{4} \times 6^2 = 54\sqrt3$
Total curved surface area of prism = 2 × (Area of base) + 6 × (Side of the base) × height
⇒ $216\sqrt3 = 2 \times 54\sqrt3 + 6 \times 6 \times h$
⇒ $108\sqrt3 = 36h$
$\therefore h = 3\sqrt3\ \text{cm}$
Hence, the correct answer is $3\sqrt3$.
Related Questions
Know More about
Staff Selection Commission Combined Grad ...
Answer Key | Eligibility | Application | Selection Process | Preparation Tips | Result | Admit Card
Get Updates Brochure
Your Staff Selection Commission Combined Graduate Level Exam brochure has been successfully mailed to your registered email id “”.
