Subject: General Aptitude · Chapter: Volume and Surface Area · Exam: 2006 · Marks: · Difficulty:
A semicircular sheet of paper of diameter 28 cm is bent to cover the exterior surface of an open conical ice-cream cup. The depth of the ice-cream cup is
(a)8.12 cm
(b)10.12 cm
(c)12.12 cm
(d)14.12 cm
Answer
Answer (as printed): C
Explanation
Slant height of the cup, $l=$ Radius of sheet = 14 cm. Circumference of the base = Circumference of the paper sheet $=\left(\frac{22}{7} \times 14\right) \mathrm{cm}=44 \mathrm{cm}$. Let the radius of the base of the cone be $r \mathrm{cm}$. $$\therefore 2 \pi r=44 \Rightarrow r=\frac{44 \times 7}{2 \times 22}=7 .$$ Height, $h=$ $$\sqrt{l^{2}-r^{2}}=\sqrt{(14)^{2}-7^{2}}=\sqrt{147}=7 \sqrt{3} \mathrm{cm}=12.12 \mathrm{cm} .$$