Multiple choice

A toy is of the shape of a cone over a hemisphere. The radius of the hemisphere is 3 cm. The total height of the toy is 7 cm. What is the total area of the toy?

  1. 103.7 sq. cm

  2. 214.5 sq. cm

  3. 215.4 sq. cm

  4. None of these
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The toy consists of a hemisphere (radius 3) and a cone (radius 3, height 7-3=4). Surface area = 2*pi*r^2 + pi*r*l, where l = sqrt(3^2 + 4^2) = 5. Area = 2*pi*9 + pi*3*5 = 18*pi + 15*pi = 33*pi. 33 * 3.14159 = 103.67, which rounds to 103.7.

AI explanation

The total area of the toy is the sum of the curved surface area of the hemisphere and the curved surface area of the cone, using the formulas 2 * pi * r^2 and pi * r * l. The height of the cone is 7 - 3 = 4 cm, making its slant height l = sqrt(3^2 + 4^2) = 5 cm. The total surface area is 2 * (22/7) * 3^2 + (22/7) * 3 * 5 = 56.57 + 47.14 = 103.7 sq cm.

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