A toy is formed by placing a solid circular cone on a solid hemisphere and the radius of the common base of the cone and the hemisphere is 15 cm. If the volume of the toy is 2850 π then find the total surface area of that toy.
Show answer & explanation
Correct answer: C
Explanation
The correct answer is option 3 i.e.705π cm3
If the volume of the toy is 2850 π cm³.
volume of the toy = volume of cone + volume of hemisphere
2850π = 1/3 × π × radius 2 × height + 2/3 × π × radius3
2850π = 1/3 × π × 152 x height +2/3 × π × 153
2850 = 1/3 × 225 × height + 2/3 × 3375
2850 =75 × height + 2 ×1125
2850 = 75 × height + 2250
2850 - 2250 = 75 × height
600 =75 × height
height = 8 cm
total surface area of that toy = lateral surface area of cone + curved surface area
of hemisphere
= π × radius × √(radius2 + height2) + 2 × π × radius2
= π × 15 × √(152 +82) +2 × π × 15²
= π × 15 × √(225 + 64) + 2 × π × 225
= π × 15 × √(289 + 450) × π
= π × 15 ×17 + 450 x π
= 255 × π + 450 × π
= 705 π cm²