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Pranay SB

· started a discussion

· 1 Months ago

Nice problem (Question: 111695.0 )

all the best.

Question:
The diameter of a right conical tent is 6 m. If a pole of length 2 m can be fixed up in the tent at the half the distance of the radius from the centre of the base then the area of the canvas required is:

Options:
A) 10\(\pi\)
B) 12\(\pi\)
C) 15\(\pi\)
D) 16\(\pi\)
Solution:
Ans: (c)

From similar \(\triangle\)ADC and \(\triangle\)CFO


\(\cfrac{AD}{OF}=\cfrac{DC}{OC}\)

or  \(\cfrac{h}{2}=\cfrac{3}{1.5}\)      

or h = 4 cm

Slant height l = \(\sqrt{r^2+h^2}\)      

= \(\sqrt{3^2+4^2}\) 

= \(\sqrt{9+16}\)  = 5

Hence, area of canvas required = \(\pi\) rl

= \(\pi\) × 3 × 5 = 15 \(\pi\) 

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