Question

Alandra's rectangular cake pan is 33cm by 23 cm. She has enough cake batter to fill it to a depth of 3 cm. Instead, Alandra wants to pour the batter into ice cream cones. She plans to fill each cone to a depth of 9 cm with a diameter of 4 cm. How many whole cones can Alandra fill?

Answer 1

Alandra can fill 60 whole cones

Explanation:

The volume of a rectangular prism is V = L × W × H, where

• L is its length

• W is its width

• H is its height

The volume of the cone is V =
`(1)/(3)` π r² h, where

• r is the radius of its base

• h is its height

∵ Alandra's rectangular cake pan is 33 cm by 23 cm

∴ L = 33 cm and W = 23 cm

∵ She has enough cake batter to fill it to a depth of 3 cm.

∴ H = 3 cm

→ Find the volume of the batter using the 1st rule above

∵ V = 33 × 23 × 3

∴ V = 2277 cm³

∵ Alandra wants to pour the batter into ice cream cones

∵ She plans to fill each cone to a depth of 9 cm with a diameter of 4 cm

∴ h = 9 cm

∵ r =
`(1)/(2)` diameter =
`(1)/(2)` (4)

∴ r = 2 cm

→ Substitute them in the 2nd rule above to find the volume of each cone

∵ V =
`(1)/(3)` (π) (2)² (9)

∴ V = 12π cm³

→ To find the number of cones divide the volume of the batter by

the volume of each cone

∵ Number of cones = 2277 ÷ 12π

∴ Number of cones = 60.3993

→ We will take the whole number only because we need the whole cones

∴ Alandra can fill 60 whole cones