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1. The sum of the radius and the height of a cylinder is 19 m. The total surface area of the cylinder is 1672 m², what is the volume of the cylinder ?

A. 3080 m³

B. 2940 m³

C. 3220 m³

D. 2660 m³

Solution:

Let the radius of the cylinder be r and height be h
Then, r + h = 19
Again, total surface area of cylinder =

(2 π r h + 2 π r^{2})

Now,

\begin{aligned} 2 π r (h + r) = 1672 \\ \Rightarrow 2 π r \times 19 = 1672 \\ \Rightarrow 38 π r = 1672 \\ ∴ π r = \frac{1672}{38} = 44 m \\ ∴ r = \frac{44 \times 7}{22} = 14 m \end{aligned}

∴ Height = 19 - 14 = 5 m
Volume of cylinder :

\begin{aligned} = π r^{2} h \\ = \frac{22}{7} \times 14 \times 14 \times 5 \\ = 22 \times 2 \times 14 \times 5 \\ = 3080 m^{3} \end{aligned}

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