Multiple choice

A toy is in the shape of a right circular cylinder with a hemisphere on one end and a cone on the other. The height and radius of the cylindrical part are $13 cm$ and $5cm$, respectively. The radii of the hemispherical and conical parts are the same as that of the cylindrical part. Calculate the surface area of toy if the height of the conical part is $12 cm.$

  1. $660 cm^2$
  2. $770 cm^2$
  3. $880 cm^2$
  4. $990 cm^2$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Surface area = CSA of cylinder + CSA of hemisphere + CSA of cone. CSA_cyl = 2*pi*r*h = 2*pi*5*13 = 130*pi. CSA_hemi = 2*pi*r^2 = 2*pi*25 = 50*pi. CSA_cone = pi*r*l. Slant height l = sqrt(r^2 + h^2) = sqrt(5^2 + 12^2) = 13. CSA_cone = pi*5*13 = 65*pi. Total = (130+50+65)*pi = 245*pi. 245 * 3.14 = 769.3, which rounds to 770.

AI explanation

The toy's surface area includes the curved surfaces of the hemisphere and cone, plus the lateral surface of the cylinder. The surface area is 2*pi*5^2 + 2*pi*5*13 + pi*5*13, where 13 cm is the slant height of the cone found by the Pythagorean theorem. This becomes 50*pi + 130*pi + 65*pi = 245*pi, and using pi as 22/7 gives a total surface area of 770 square cm.

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