Multiple choice

A toy is in the shape of a cone surmounting a hemisphere of radius 21 cm if the height of the cone is 28 cm, the total surface area of the toy is

  1. $\displaystyle 4824cm^{2}$
  2. $\displaystyle 4076cm^{2}$
  3. $\displaystyle 5082cm^{2}$

  4. None
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Radius r = 21, height h = 28. Slant height l = sqrt(21^2 + 28^2) = sqrt(441 + 784) = sqrt(1225) = 35. Surface area = pi * r * l (cone) + 2 * pi * r^2 (hemisphere). SA = (22/7) * 21 * 35 + 2 * (22/7) * 21 * 21 = 2310 + 2772 = 5082.

AI explanation

The total surface area is the sum of the curved surface area of the cone and the curved surface area of the hemisphere, using the common radius of 21 cm. The cone slant height is sqrt(21^2 + 28^2) = sqrt(1225) = 35 cm. Therefore, the total area is pi * 21 * 35 + 2 * pi * 21^2 = 735 * pi + 882 * pi = 1617 * pi, which equals approximately 5082 cm^2.

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