
The diameter of a sphere is decreased by 25%. Find the percentage of decrease of its curved surface area?
Answer
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Hint: We start solving the given question by finding the curved surface area of original sphere using the formula . Then we decrease the diameter by 25% and find the curved surface area of the new sphere formed and then we find the percentage of decrease of the curved surface area from original sphere to new sphere.
Complete step-by-step answer:
Let us consider the radius of the sphere as , and let its diameter be and let its curved surface area be .
Let us use the formula for the diameter of sphere,
Then, the diameter of our given sphere in terms of radius is given by .
Using the formula for the curved surface area of the sphere,
Applying the above formula, we get
Given that the diameter of the curve is decreased by 25%.
Let the new diameter be and radius be and curved surface area be .
Then we can write in terms of as
Then as and , by substituting them in equation (1) we get,
Applying the formula for the curved surface area of the sphere again, we get the Curved Surface Area of new sphere as
So, now we can find the percentage of decrease of curved surface area as
Hence, we get that the decrease in the curved surface area is equal to 43.75%.
Hence, the answer is 43.75%.
Note: One can make a mistake while solving the problem by substituting the diameter of the new sphere in the formula of curved surface area of sphere instead of using radius of the new sphere.
Complete step-by-step answer:
Let us consider the radius of the sphere as

Let us use the formula for the diameter of sphere,
Then, the diameter of our given sphere in terms of radius is given by
Using the formula for the curved surface area of the sphere,
Applying the above formula, we get
Given that the diameter of the curve is decreased by 25%.
Let the new diameter be
Then we can write
Then as
Applying the formula for the curved surface area of the sphere again, we get the Curved Surface Area of new sphere as
So, now we can find the percentage of decrease of curved surface area as
Hence, we get that the decrease in the curved surface area is equal to 43.75%.
Hence, the answer is 43.75%.
Note: One can make a mistake while solving the problem by substituting the diameter of the new sphere in the formula of curved surface area of sphere instead of using radius of the new sphere.
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