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The curved surface of a frustum cone is $25 π m m 2$ . The larger circle area is $12 π m m 2$ . The total surface area is $350 π m m 2$ . Then the smaller circle area of a cone is?

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313 π m m 2

323 π m m 2

333 π m m 2

353 π m m 2

answer is D.

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Detailed Solution

Let's consider a frustum with height h and smaller radius r and bigger radius R
Question Image

We are given the area of the bigger circle to

12 π m m 2

.
We know that the area of circle is given by

π r 2

sq. units
Therefore
Area of bigger circle

= π R 2

sq. units

⇒ 12 π = π R 2 ⇒ 12 = R 2 .............. (1)

We are given that the curved surface area of the frustum is

25 π m m 2

We know that the curved surface area of a frustum is given by

π (r + R) h

sq. units.

⇒ π (r + R) h = 25 π ⇒ (r + R) h = 25.............. (2)

We are given that the total surface area is

350 π m m 2

.
We know that the total surface area of a frustum is given by

π (r + R) h + r 2 + R 2

square units

⇒ π (r + R) h + r 2 + R 2 = 350 π ⇒ (r + R) h + r 2 + R 2 = 350

Substitute the values from equation (1) and (2) we get

⇒ 25 + r 2 + 12 = 350 ⇒ 37 + r 2 = 350 ⇒ r 2 = 350 − 37 ⇒ r 2 = 313

Therefore
Area of smaller circle

= 313 m m 2

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