The sum of the altitude and the base radius of a cylinder is $63 c m$ $63 cm$ . The radius is $\frac{4}{5}$ $4/5$ as long as the altitude. Calculate the surface area volume of the cylinder?

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Answer 1 · 2016-05-28T01:52:09

Let y be the altitude, and x be the radius.

$x + y = 63$ $x + y = 63$

$\frac{4}{5} y = x$ $4/5y = x$

$\frac{4}{5} y + y = 63$ $4/5y + y = 63$

$\frac{9 y}{5} = 63$ $(9y)/5 = 63$

$9 y = 63 \times 5$ $9y = 63 xx 5$

$9 y = 315$ $9y = 315$

$y = 35$ $y = 35$

$x + 35 = 63$ $x + 35 = 63$

$x = 63 - 35$ $x = 63 - 35$

$x = 28$ $x = 28$

The surface area of a cylinder is given by $S . A = 2 r^{2} π + 2 r h π$ $S.A = 2r^2pi + 2rhπ$

The radius, r, measures 28 cm.

Therefore, $S . A = 2 {(28)}^{2} π + 2 (28) (35) π$ $S.A = 2(28)^2pi + 2(28)(35)π$

$S . A = 1568 π + 1960 π$ $S.A = 1568pi + 1960pi$

$S . A = 3528 π$ $S.A = 3528pi$ c $m^{2}$ $m^2$

As for the volume, the volume of a cylinder is given by $V = r^{2} π \times h$ $V = r^2π xx h$

$V = 28^{2} π \times 35$ $V = 28^2pi xx 35$

$V = 27440 π$ $V = 27440pi$ c $m^{3}$ $m^3$

Hopefully this helps!

The sum of the altitude and the base radius of a cylinder is 63 cm63cm63 cm. The radius is 4/5454/5 as long as the altitude. Calculate the surface area volume of the cylinder?