Question

A conical cup when completely filled with ice cream forms a hemispherical shape on its open end. What is the volume of ice cream. If the radius of base of the cone is 3.5 cm and the vertical height of the cone is 9 cm?
1. 1643 cm³
2. 1523 cm³
3. 2365 cm³
4. 1203 cm³

Answer 1

Correct Answer - Option 1 : 1643 cm³

Given:

The radius of the cone 3.5 cm

The vertical height  of the cone 9 cm

Concept:

The volume of the cone = (1/3) × (π × r² × h) 

Calculation:

⇒ Volume of the cone = (1/3) × (22/7) × (3.5 × 3.5 × 9) = 115.5

⇒ Volume of the hemispherical portion of ice cream = (2/3) × (π × r³)

⇒ (2/3) × (22/7) × (9³) = 1527.42 ≈ 1527.5

⇒ Total volume of icecream = 115.5 + 1527.5 = 1643

∴ The required result will be 1643 cm³.