Multiple choice

Find the curved surface area of a cylinder if the radius of the cylinder is twice the radius of a cone whose curved surface area is 110 m2 and the latent height is 7 m. Also, height of the cylinder is equal to that of cone. (Take approximate values.)

  1. 298 m2

  2. 300 m2

  3. 305 m2

  4. 308 m2

  5. 316 m2
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D Correct answer
Explanation

The cone radius is 110 divided by pi times 7, which is approximately 5 m. Its height is sqrt(7^2 - 5^2), approximately 4.9 m, so the cylinder radius is about 10 m. Its curved surface area is approximately 2pi times 10 times 4.9 = 308 m^2.

AI explanation

Using the curved surface area of a cone formula, pi times r times l equals 110. With a slant height of 7, this gives pi times r equals 110 divided by 7. The cylinder radius is twice the cone radius, so it is 22 divided by 7, and the cylinder height equals the cone height. Using the Pythagorean theorem, the cone height is the square root of 7 squared minus r squared, which is approximately 6.24 m. The curved surface area of the cylinder is 2 times pi times R times H, calculated as 2 times 3.1416 times 3.1428 times 6.24, resulting in approximately 308 m2.

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