Question : The volume of a conical tent is 1232 m3 and the area of its base is 154 sq m. Find the length of the canvas required to build the tent, if the canvas is 2 m in width. (Take $\pi=\frac{22}{7}$)
Option 1: 270 m
Option 2: 272 m
Option 3: 276 m
Option 4: 275 m
Correct Answer: 275 m
Solution :
Let the radius be $r$ and the height be $h$.
Area of the base = 154 sq m
⇒ $\pi r^2$ = 154
$\therefore r$ = 7 m
Volume of cone = $\frac{1}{3}\pi r^2 h$
⇒ $1232 =\frac{1}{3}×\frac{22}{7}×7×7×h$
$\therefore h = 24$ m
Slant height, $l$ = $\sqrt{h^2+r^2}$ = $\sqrt{24^2+7^2}$ = $\sqrt{625}= 25$ m
$\therefore$ Area of the canvas $=\pi r l=\frac{22}{7}×7×25 = 550$ m
2
Length of the canvas required to cover conical tent of width 2 m = $\frac{550}{2}$ = 275 m
Hence, the correct answer is 275 m.
Related Questions
Know More about
Staff Selection Commission Combined Grad ...
Admit Card | Eligibility | Application | Selection Process | Preparation Tips | Result | Answer Key
Get Updates Brochure
Your Staff Selection Commission Combined Graduate Level Exam brochure has been successfully mailed to your registered email id “”.
