Question

The internal and external diameter of a hollow hemispherical vessel are 20cm and 28cm resp. find the cost of painting the vessel all over at 14 paise per cm^2.

Answer 1

cost of painting of vessel = 302.70 Rs.
$\frac{15136}{7} \times 14 = 30272 \: paise = 302.72 \: rupees$

Answer 2

Answer: Rs. 302.7192

Step-by-step explanation:

Given : internal diameter = 20 cm

external diameter = 28 cm

Therefore internal radius; R= 10cm

External radius; r= 14 cm

Total surface area= curved surface area of internal hemisphere + curved surface area of outer hemisphere + area of ring

Now as we know Curved surface area of hemisphere is $2\pi r^2$

Now curved surface area of internal hemisphere is

$C.S.A= 2\pi R^2 = 2\times \dfrac{22}{7} \times14 \times 14 = 1232cm^2----(i)$

Now curved surface area of outer hemisphere

$C.S.A= 2\pi r^2 = 2\times \dfrac{22}{7} \times10 \times 10 = 628.57cm^2----(ii)$

area of ring = area of outer circle -area of inner circle

$\text {Area of ring} = \pi R^2- \pi r^2= \dfrac{22}{7} (R^2-r^2)\\\\= \dfrac{22}{7} (14^2-10^2)= 301.71 cm^2----(iii)$

(i)+(ii)+(iii) we get

Total surface area= curved surface area of internal hemisphere + curved surface area of outer hemisphere + area of ring = 1232+ 628.57+ 301.71 = 2162.28cm²

Cost of per cm² = 14p

cost of 2162.28cm²= 14 x 2162.28=30271.92p = Rs. 302.7192

Hence, the cost of painting the vessel is Rs. 302.7192