Question : What will be the difference between the total surface area and the curved surface area of a hemisphere having a 4 cm diameter in cm2?
Option 1: $5\pi $
Option 2: $8\pi $
Option 3: $4\pi $
Option 4: $4.4\pi $
Correct Answer: $4\pi $
Solution : The total surface area of a hemisphere = $3\pi r^2$ The curved surface area a hemisphere = $2\pi r^2$ where $r$ is the radius of the hemisphere. Given that the diameter of the hemisphere is 4 cm, the radius $r$ is 2 cm. The total surface area of a hemisphere = $3\pi (2)^2 = 12\pi$ cm2 The curved surface area a hemisphere = $2\pi (2)^2 = 8\pi$ cm2 Therefore, the difference between the total surface area and the curved surface area of the hemisphere is: Difference = TSA – CSA = $12\pi - 8\pi = 4\pi$ cm2 Hence, the correct answer is $4\pi$.
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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
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 total surface area of a right circular cylinder is 1848 cm2. The ratio of its total surface area to the curved surface area is 3 : 1. The volume of the cylinder is: (Take $\pi=\frac{22}{7}$)
Option 1: 4312 cm3
Option 2: 3696 cm3
Option 3: 4002 cm3
Option 4: 4851 cm3
Question : The total surface area of a hemisphere is 462 cm2. The diameter of this hemisphere is:
Option 1: 28 cm
Option 2: 21 cm
Option 3: 7 cm
Option 4: 14 cm
Question : The diameter of a hemisphere is equal to the diagonal of a rectangle of length 4 cm and breadth 3 cm. Find the total surface area (in cm²) of the hemisphere.
Option 1: $25 \pi$
Option 2: $\frac{75 \pi}{4}$
Option 3: $\frac{50 \pi}{4}$
Option 4: $\frac{25 \pi}{4}$
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