question_answer

The area of the curved surface of a right circular  cone of diameter 14 cm is \[\text{55}0\text{ c}{{\text{m}}^{\text{2}}}\] The height of the cone is

A)  25 cm             

B)         22 cm

C)  23 cm                  

D)  24 cm  

Correct Answer: D

Solution :

 \[r=\frac{14}{2}=7cm.\] Let h be the height of the cone      Then, curved surface \[=\pi \,rl\]                                                 \[=pr\sqrt{{{r}^{2}}+{{h}^{2}}}\]                 \[=\pi \times 7\times \sqrt{{{7}^{2}}+{{h}^{2}}}\] By hypothesis, \[7\pi \sqrt{49+{{h}^{2}}}\]                 \[=550\] or            \[\sqrt{49+{{h}^{2}}}=\frac{550}{7\pi }=\frac{550}{7\times \frac{22}{7}}=25\] or            \[49\times {{h}^{2}}={{25}^{2}}=625\] or            \[{{h}^{2}}=576\] or            \[h=24cm\]