Question

A toy is a combination of a cylinder, hemisphere and a cone, each with radius $10cm$ as shown in the figure. Height of the conical part is $10cm$ and total height is $60cm$. Find the total surface area of the toy $(\pi =3.14,\sqrt{2}=1.41)$.

• A. $4882.74c{m}^2$
• B. $4382.74c{m}^2$
• C. $3582.74c{m}^2$
• D. $35982.74c{m}^2$

Answer 1

Answer: (C)

$3582.74c{m}^2$

Given, toy is combination of cylinder, hemisphere and cone with radius $10$ cm. Height of conical part is $10$ cm and total height is $60$ cm.
So,height of cylindrical part$=$ Total height $-$ height of conical part $-$ radius of the hemisphere
$=60$ cm $-10$ cm -$10$ cm
$=40$ cm.
Slant height of conical figure,$l=\sqrt{h^2+r^2}=\sqrt{{10}^2+{10}^2}=\sqrt{200}=10\sqrt{2}=10\times 1.41=14.1cm$
Total surface area of toy $=$ curved surface area of cone + curved surface area of cylinder + curved surface area of hemisphere
$=\pi rl+2\pi rh+2\pi r^2=3.14\times 10\times 14.1+2\times 3.14\times 10\times 40+2\times 3.14\times {10}^2=442.74{cm}^2+2512{cm}^2+628{cm}^2=3582.74{cm}^2$