Multiple choice

A toy is a in the form of a cone mounted on a hemisphere of base radius 3.5 cm. If the total height of the toy is 15.5 cm. Find its total surface area of the toy. (Use π=22/7)

  1. 218.50

  2. 314

  3. 137.5

  4. 214.50
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

The cone's height is 15.5 - 3.5 = 12 cm, so its slant height is sqrt(12^2 + 3.5^2) = 12.5 cm. The exposed area is πrl + 2πr^2 = (22/7)(3.5)(12.5 + 7) = 214.5 cm^2.

AI explanation

The height of the conical part is the total height minus the hemisphere's radius, giving 15.5 - 3.5 = 12 cm, and using the slant height formula l = sqrt(r^2 + h^2) gives l = sqrt(3.5^2 + 12^2) = 12.5 cm. The total surface area formula for this toy is curved surface area of the cone plus curved surface area of the hemisphere, written as pi*r*l + 2*pi*r^2. Substituting the values gives (22/7)3.5(12.5 + 2*3.5) = 11*19.5 = 214.50 square cm.

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