A toy is in the form of a hemisphere surmounted by a right circular cone of the same base radius as that of the hemisphere. If the radius of the base of the cone is 21 cm and its volume is 2/3 of the volume of the hemisphere, calculate the height of the cone and the surface area of the toy.(Use π=22/7)
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Height of the cone = 28 cm
Total surface area of toy = 5082 sq.cm
Step-by-step explanation:
Radius of cone = radius of hemisphere = 21cm
Volume of cone = 2/3 volume of hemisphere
πr²h/3 = 2/3 * (2/3) π r³
h = 2/3 * 2 * r
= 4/3 * 21
height of the cone = 28 cm
slant height of cone = root of (28² + 21²) = root (784 + 441) = root 1225 = 35 cm
Curved Surface area of cone = πrl
Curved Surface area of hemisphere = 2πr²
Total surface area of toy = πrl + 2πr² = πr (l +2r) = 22/7 * 21 (35 + 42)
= 66(77)
= 5082 sq.cm
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