Question : A conical-shaped vessel has a radius of 21 cm and a slant height of 25 cm. If the curved part of the vessel is to be painted white, find the cost (in Rs. ) of painting at the rate of Rs. 1.5 per cm2.
Option 1: 2475
Option 2: 1650
Option 3: 825
Option 4: 1250
Correct Answer: 2475
Solution :
The curved surface area (CSA) of a cone is given by the formula:
$\text{CSA} = \pi r l$
Where $r$ is the radius and $l$ is the slant height.
Given that the radius $r$ is 21 cm and the slant height $l$ is 25 cm.
$\text{CSA} = \pi \times 21 \, \text{cm} \times 25 \, \text{cm} = 525\pi \, \text{cm}^2$
The cost of painting the curved part of the vessel is calculated by multiplying the CSA by the cost per square cm.
Given that the cost of painting is Rs. 1.5 per cm
2
, the total cost of painting $= 525\pi \times 1.5 = 525\times \frac{22}{7}\times 1.5= \text{Rs.}\;2475$
Hence, the correct answer is 2475.
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