ABC26GN4954 · Volume and Surface Area
Subject: General Aptitude · Chapter: Volume and Surface Area · Exam: · Marks: · Difficulty:
The radius and height of a right circular cone are in the ratio 3 : 4. If its volume is $301 \frac{5}{7} \mathrm{cm}^{3}$, what is its slant height?
(a)8 cm
(b)9 cm
(c)10 cm
(d)12 cm
Answer
Explanation
Let the radius and height of the cone be $3 x$ and $4 x$ respectively. Then, $$\begin{gathered} \frac{1}{3} \times \frac{22}{7} \times(3 x)^{2} \times 4 x=\frac{2112}{7} \Leftrightarrow \frac{264}{7} x^{3}=\frac{2112}{7} \Leftrightarrow x^{3}=\frac{2112}{64}=8 \\ \Leftrightarrow x=2 . \\ \therefore \text { Radius }=6 \mathrm{cm}, \text { Height }=8 \mathrm{cm} . \text { Slant height } \\ =\sqrt{6^{2}+8^{2}} \mathrm{cm}=\sqrt{100} \mathrm{cm}=10 \mathrm{cm} . \end{gathered}$$
Open in whiteboard · Browse this chapter in the app