If the radii of the ends of a bucket, 45 cm high, are 28 cm and 7 cm respectively, then the total surface area of the bucket in sq.cm is:
8074

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Solution

The correct option is A 8074

Total surface area of the bucket
$= T S A = π \times l \times (r_{1} + r_{2}) + π \times ({r_{1}}^{2} + {r_{2}}^{2})$

Where $π = \frac{22}{7},$
$l =$ Slant height of the bucket
$= \sqrt{(h)^{2} + (r_{1} - r_{2})^{2}}$

$r_{1} = 28 c m$ and $r_{2}$ = 7 cm

$l =$ Slant height of the bucket
$= \sqrt{(45)^{2} + (21)^{2}} c m = 49.6 c m$

Therefore,
$T S A = [\frac{22}{7} \times 49.6 \times (28 + 7) + \frac{22}{7} \times (28^{2} + 7^{2})] c m^{2} = 8074 c m^{2}$

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