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Answer :
Final answer:
To calculate the total volume of ice-cream in a cone with a hemispherical topping, you sum the volume of the cone and the volume of the hemisphere, but the answer doesn't match the provided options.
Explanation:
The student asked for the volume of the ice-cream in a cone with a hemispherical topping. The cone has a radius of 3.5 cm and a height of 8 cm.
To find the total volume, we calculate the volume of the cone using the formula V = πr²h and add it to the volume of the hemispherical topping, calculated with the formula V = ²/3πr3 since half a sphere is involved.
- Volume of the cone = π × (3.5 cm)2 × 8 cm = 98π cm3
- Volume of the hemisphere = ²/3π × (3.5 cm)3 = ²/3 × 43.75π cm3 = 29π cm3
- Total volume = Volume of the cone + Volume of the hemisphere = 98π cm3 + 29π cm3 = 127π cm3
Using the approximation π = 3.14, we get the total volume as approximately 127 × 3.14 cm3, which equals 398.78 cm3.
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