Question

A scoop of ice cream is the shape of a whole perfect sphere sits in a right cone.

Answer 1

Answer:

$\large \boxed{\text{10 cm}}$

Step-by-step explanation:

The volume of the sphere must equal  the volume of the cone.

$\begin{array}{rcll}V_{\text{sphere}} & = & V_{\text{cone}}&\\\dfrac{4}{3} \pi r^{3}& = & \dfrac{1}{3} \pi r^{2} h&\\4 \pi r^{3} & = & \pi r^{2} h &\text{Multiplied each side by 3}\\4r & = & h&\text{Divided each side by }\pi r^{2}\\h & = & 4r \times 2.5&\text{Substituted the value of }r\\& = & \textbf{10 cm}&\\\end{array}\\\text{The height of the cone must be \large \boxed{\textbf{10 cm}} }$

Answer 2

Answer:

  10 cm

Step-by-step explanation:

The volume of a sphere is given by the formula ...

  V = 4/3πr³

The volume of a cone is given by the formula ...

  V = 1/3πr²h

The ratio of the volume of the cone to that of the sphere is ...

  Vcone/Vsphere = (1/3πr²h)/(4/3πr³) = h/(4r)

In order for the ratio to have a value of 1, we must have ...

  h = 4r

The height of the cone must be 4×2.5 cm = 10 cm to fit all of the ice cream.