Subject: General Aptitude · Chapter: Volume and Surface Area · Exam: · Marks: · Difficulty:
A solid cylindrical block of radius 12 cm and height 18 cm is mounted with a conical block of radius 12 cm and height 5 cm. The total lateral surface of the solid thus formed is
(a)$528 \mathrm{cm}^{2}$
(b)$1357 \frac{5}{7} \mathrm{cm}^{2}$
(c)$1848 \mathrm{cm}^{2}$
(d)None of these
Answer
Answer (as printed): D
Explanation
Slant height of the cone, $l=\sqrt{(12)^{2}+(5)^{2}}=13 \mathrm{cm}$. Lateral surface of the solid = Curved surface of cone + Curved surface of cylinder + Surface area of bottom $$\begin{aligned} & =\pi r l+2 \pi r h+\pi r^{2}, \text { where } h \text { is the height of the cylinder } \\ & =\pi r(l+h+r)=\left[\frac{22}{7} \times 12 \times(13+18+12)\right] \mathrm{cm}^{2} \\ & =\left(\frac{22}{7} \times 12 \times 43\right) \mathrm{cm}^{2}=\left(\frac{11352}{7}\right) \mathrm{cm}^{2}=1621 \frac{5}{7} \mathrm{cm}^{2} . \end{aligned}$$