Question 54

If the volume and curved surface area of a cylinder are 616 $$m^3$$ and 352 $$m^2$$ respectively what is the total surface area of the cylinder (in $$m^2$$)


Volume of a cylinder=$$\pi \times r^{2} \times h$$
where $$r$$ and $$h$$ are the radius and height of the cylinder.
$$\pi \times r^{2} \times h$$ = $$616 m^{3}$$
Curved Surface Area of Cylinder=$$2\times \pi \times r \times h$$=$$352 m^{2}$$
$$\pi \times r \times h$$=$$176$$
Replacing $$\pi \times r \times h$$ in Volume formula we get,
$$ r \times 176$$=$$616$$
$$r=3.5 m$$
Total Surface Area = Curved Surface Area + 2$$\times$$ Area of base
=$$352 + 2\times pi \times r^{2}$$
=$$352 + 2\times pi \times 3.5^{2}$$
=$$429 m^{2}.$$
Hence Option A is the correct answer.

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