ABC26GN4951 · Volume and Surface Area
Subject: General Aptitude · Chapter: Volume and Surface Area · Exam: · Marks: · Difficulty:
The slant height of a conical mountain is 2.5 km and the area of its base is $1.54 \mathrm{km}^{2}$. The height of the mountain is
(a)2.2 km
(b)2.4 km
(c)3 km
(d)3.11 km
Answer
Explanation
Let the radius of the base be $r \mathrm{km}$. Then, $$\pi r^{2}=1.54 \Rightarrow r^{2}=\left(\frac{1.54 \times 7}{22}\right)=0.49 \Rightarrow r=0.7 \mathrm{km} .$$ Now, $l=2.5 \mathrm{km}, r=0.7 \mathrm{km}$. $$\begin{aligned} \therefore h=\sqrt{(2.5)^{2}-(0.7)^{2}} \mathrm{km}=\sqrt{6.25-0.49} \mathrm{km} & =\sqrt{5.76} \mathrm{km} \\ & =2.4 \mathrm{km} . \end{aligned}$$ So, height of the mountain $=2.4 \mathrm{km}$.
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