Question

The front compound wall of a house is decorated by wooden spheres of a diameter $21cm$, placed on small supports as shown in the figure. Eight such spheres are used for this purpose and are to be painted silver. Each support is a cylinder of radius $1.5cm$ and height $7cm$ and is to be painted black. Find the cost of paint required if silver paint costs $25paiseperc{m}^2$.

Answer 1

$r=\frac{21}{2}=10.5$cm, SA$=4\pi r^2$
$=4\times \frac{22}{7}\times {\left(10.5\right)}^2$
$=1386$cm${}^2$
Cylindrical support,
$r_1$ of circular end$=1.5$cm, $h=7$cm
Curved Surface Area $=2\pi rh=2\times \frac{22}{7}\times 1.5\times 7=66$cm${}^2$
Area of circular end $=\pi r^2=\frac{22}{7}\times {\left(1.5\right)}^2=7.07$ cm${}^2$
Area to be painted silver $=8\times (1386-7.07)$cm${}^2$
$=8\times 1378.9=11031.44$cm${}^2$
Cost of silver color $=$Rs.$0.25\times 11031.4$
$=$Rs.$2757.8$
Area to be painted black $=8\times 66=578$cm${}^2$
Cost of painting black color$=1528\times 0.05$
$=$Rs.$26.40$
Total cost $=$Rs.$2757.8+26.4$
$=$Rs.$2784.2$