Multiple choice

The diameter of the base of metallic cone is $2$ cm and height is $10$ cm. $900$ such cones are molten to form 1 right circular cylinder whose radius is $10$ cm. Find total surface area of the right circular cylinder so formed. (Given $\pi$ = 3.14)

  1. $2510$ c$m^2$
  2. $2512$ $cm^2$
  3. $2515$ $cm^2$
  4. $2530$ $cm^2$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Volume of 900 cones = 900 * (1/3 * pi * 1^2 * 10) = 3000 * pi. Cylinder volume = pi * 10^2 * h = 100 * pi * h. So h = 30. Total surface area = 2 * pi * r * (h + r) = 2 * 3.14 * 10 * (30 + 10) = 2512.

AI explanation

The total volume of the 900 cones is equal to the volume of the newly formed cylinder, represented by 900 * (1/3) * pi * 1^2 * 10 = pi * 10^2 * h. Solving for the cylinder's height gives h = 30 cm. Using the total surface area formula 2 * pi * r * (r + h), we get 2 * 3.14 * 10 * (10 + 30), which equals 2512 square cm.

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