Subject: General Aptitude · Chapter: Volume and Surface Area · Exam: · Marks: · Difficulty:
Each of the measures of the radius of the base of a cone and that of a sphere is 8 cm . Also, the volumes of these two solids are equal. The slant height of the cone is
(a)34 cm
(b)$34 \sqrt{2} \mathrm{cm}$
(c)$4 \sqrt{17} \mathrm{cm}$
(d)$8 \sqrt{17} \mathrm{cm}$
Answer
Answer (as printed): D
Explanation
Let the height of the cone be $h$ cm. Then, $\frac{1}{3} \pi \times 8^{2} \times 4=\frac{4}{3} \pi \times 8^{3} \Rightarrow h=32 \mathrm{cm}$. ∴ Slant height, $l=$ $$\sqrt{h^{2}+r^{2}}=\sqrt{(32)^{2}+8^{2}}=\sqrt{1088}=8 \sqrt{17} \mathrm{cm} .$$