2. A scoop of ice cream in the shape of a whole perfect sphere sits in a right cone.
The radius of the ice cream scoop is 2.5cm and the radius of the cone is 2.5cm.
How tall must the height of the cone be to fit all the ice cream without spilling if it melts?
Answer (Show Work):

10 cm.

Step-by-step explanation:

The volume of the cone must be equal to the volume of the sphere for there to be no spillage.

The volume of the sphere = 4/3 π r^3 cm^3

= 4/3 * 2.5^3 π  cm^3

The volume of the cone = 1/3 π 2.5^2 h  where h is the height of the cone.

So:   4/3 * 2.5^3 π  =  1/3 π 2.5^2  h

h =  (4/3 * 2.5^3) π  /  (1/3 *2.5^2)π

= 4 * 2.5

= 10 cm.

let x be the money she spent so that she can earn the free t-shirt.

since, she already spent $112.49

⇒

also, as per the statement: jennifer must spend $250 or more in order to qualify for a free t-shirt at the store.

then,

we have an inequality i.,e

subtract 112.49 from both sides we get;

therefore, $137. 51 more money does jennifer need to spend so that she can earn the free t-shirt