The circumference of the base of a conical tent is 66 m. If the height of the tent is 36 m, what is the area (in m2) of the canvas used in making the tent? (Take π = $\frac{22}{7}$)
Answer & explanation
Correct answer: option 1
We know that,
Curved surface area of conical tent = πrl
Circumference of the base of a conical tent = 2πr
l2 = r2 + h2
We have,
Height of the conical tent h = 36 m
According to the question,
2 πr = 66
= 2 × \(\frac{22}{7}\) × r = 66
= r = 66 × \(\frac{7}{44}\)
= r = \(\frac{21}{2}\)
As we know,
= l2 = (\(\frac{21}{2}\))2 + 362
= l2 = \(\frac{441}{4}\) + 1296
= l2 = \(\frac{5625}{4}\)
= l = \(\frac{75}{2}\)
Now, Curved surface area of conical tent = \(\frac{22}{7}\) × \(\frac{21}{2}\) × \(\frac{75}{2}\) = 1237.5 m2