Question

A scoop of ice cream in the shape of a whole sphere sits in a right cone. The radius of the ice cream scoop is 2. 5 cm and the radius of the cone is 2. 5 cm. How tall must the height of the cone be to fit all the ice cream without spilling if it melts? show all your work.

Answer 1

The height of the cone to fit all the ice cream without spilling if it melts is 10 cm

How to find the height of the cone

• radius, r of ice cream scoop = 2.5 cm

• radius, r of cone = 2.5 cm

Volume of the ice cream scoop = 4/3πr³

= 4/3 × 3.14 × 2.5³

= 4/3 × 3.14 × 15.625

= 65.4166666666666 cm³

Approximately,

65.42 cm³

Volume of the cone = 1/3πr²h

= 1/3 × 3.14 × 2.5² × h

= 1/3 × 3.14 × 6.25 × h

= 6.54166666666666h cm³

Approximately,

6.54h cm³

• Equate both volume

65.42 cm³ = 6.54h cm³

h = 65.42 / 6.54

= 10.0030581039755 cm

Approximately,

h = 10 cm

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