Question

From a closed cardboard cylinder of height 30 cm and diameter of base 21 cm, 15 rectangles of size 2 cm $\times$ 1.5 cm are cut out. Find the total surface area of the remaining cylinder.

Answer 1

Given:Height of the cylinder$=30$cm

Base diameter of the cylinder$=21$cm

Base radius of the cylinder$=\frac{21}{2}$cm

Total Surface area of the cylinder$=2\pi r(r+h)$sq.cm

$=2\times \frac{22}{7}\times \frac{21}{2}(\frac{21}{2}+30)$sq.cm

$=\frac{2\times 22\times 21\times (21+60)}{7\times 2}$

$=11\times 3\times 81=2673$ sq.cm(on simplification)

Given that a closed cardboard cylinder is made in to $15$ rectangles

Area of one rectangle$=l\times b=2\times 1.5=3$sq.cm

Area of $15$ rectangle$=3\times 15=45$sq.cm

Remaining cardboard $=$T.S.A of cylinder$-$Area of the rectangle

$=2673-45=2628$sq.cm