Question:
The curved surface area of a cone is $4070 \mathrm{~cm}^{2}$ and diameter is $70 \mathrm{~cm}$. What is its slant height?
Solution:
Diameter of the cone (d) = 70 cm
Radius of the cone $(\mathrm{r})=\mathrm{d}^{2}=35 \mathrm{~cm}$
Slant height of the cone (l) = ?
Now,
Curved Surface Area $=4070 \mathrm{~cm}^{2}$
$\Rightarrow \pi r \mid=4070$
Where, r = Radius of the cone
l = Slant height of the cone
Therefore πrl = 4070
⟹ 22/7 ∗ 35 ∗ l = 4070
$\Rightarrow \mathrm{l}=\frac{4070 * 7}{22 * 35}=37 \mathrm{~cm}$
Therefore slant height of the cone is 37 cm.
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