A toy is in the form of a cone mounted on a hemisphere. The radius of the hemisphere and that of the cone is 36 cm and height of the cone is 105 cm. The total surface area (in cm2) of the toy is:
Show answer & explanation
Correct answer: C
Explanation
The correct answer is option 3 i.e. 6588 π.
Radius of the hemisphere or cone (r) = 36 cm
Height of the cone (h) = 105 cm
Slant height of cone l = √(r2 + h2) = √(362 + 1052) = √(1296 + 11025) = √12321 = 111 cm
Curved surface area of the cone = πrl = π × 36 × 111 = 3996π cm2
Curved surface area of the hemisphere = 2πr2 = 2 × π × 362 = 2592π cm2
Total surface area of the toy = 3996π + 2592π = 6588π cm2
Therefore, the total surface area of the toy is 6588π cm2.