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 cm2, 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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Question : The curved surface area of a cone whose base radius is 7 cm and slant height is 10 cm is:
Option 1: 280 cm2
Option 2: 250 cm2
Option 3: 300 cm2
Option 4: 220 cm2
Question : The curved surface area (CSA) and the total surface area (TSA) of a hemisphere whose radius is 7 cm are:
Option 1: CSA – 350 cm2; TSA – 500 cm2
Option 2: CSA – 320 cm2; TSA – 480 cm2
Option 3: CSA – 412 cm2; TSA – 544 cm2
Option 4: CSA – 308 cm2; TSA – 462 cm2
Question : What is the difference between the total surface area and the curved surface area of a cone whose radius is 35 cm? (Take $\pi=\frac{22}{7}$)
Option 1: 3850 cm2
Option 2: 3704 cm2
Option 3: 3750 cm2
Option 4: 3675 cm2
Question : The area of a sector of a circle of radius 8 cm, formed by an arc of length 4.6 cm, is ____.
Option 1: 6.3 cm2
Option 2: 9.2 cm2
Option 3: 18.4 cm2
Option 4: 12.6 cm2
Question : A hemisphere has a 42 cm diameter. Find its curved surface area and the total surface area.
Option 1: 2772 cm2 and 4158 cm2
Option 2: 3772 cm2 and 5158 cm2
Option 3: 4770 cm2 and 4238 cm2
Option 4: 3072 cm2 and 4058 cm2
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