Question

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 is:

• A. 6074 $c{m}^2$
• B. 7074 $c{m}^2$
• C. 8074 $c{m}^2$
• D. 8274 $c{m}^2$

Answer 1

The correct option is C 8074 $c{m}^2$

Total surface area of the bucket
$=TSA=\pi \times l\times (r_1+r_2)+\pi \times ({r_1}^2+{r_2}^2)$

Where $\pi =\frac{22}{7},$
$l=$ Slant height of the bucket
$=\sqrt{(h{)}^2+(r_1-r_2{)}^2}$

$r_1=28cm$ and $r_2$ = 7 cm

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

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