Question

The internal and external radii of a hollow hemispherical vessel are 12 cm and 12.5 cm respectively. If the cost for painting $1c{m}^2$ of the surface area is ₹0.05, then the total approximate cost of painting the vessel all over is $[use\pi =\frac{22}{7}]$

• A. ₹96.28
• B. ₹90.15
• C. ₹84.45
• D. ₹92.45

Answer 1

The correct option is A ₹96.28


Let the external and internal radii of hemisphere be $r_{1}and{r}_2$ respectively.

$\therefore r_1=12.5cm,r_2=12cm$

Surface area to be painted = Curved surface area of external hemisphere + Curved surface area of internal hemisphere + Area of ring

$=2\pi (r_1{)}^2+2\pi (r_2{)}^2+\pi (r_1^2-r_2^2)$

$=2\times \frac{22}{7}\left[\right(12.5{)}^2+\left(12{)}^2\right]+\frac{22}{7}\left[\right(12.5{)}^2-\left(12{)}^2\right]$

$=\frac{44}{7}[156.25+144]+\frac{22}{7}[156.25-144]$

$=\frac{22}{7}[600.5+12.25]$

$=\frac{22}{7}\times 612.75$

$=1925.78c{m}^2$

Cost for painting 1 $c{m}^2$ area = ₹0.05

⇒ Cost for painting 1925.78 $c{m}^2$ = ₹1925.78 × 0.05

= ₹96.28

Hence, the correct answer is option (a).