Answer:
Alandra can fill 60 whole cones
Step-by-step explanation:
The volume of a rectangular prism is V = L × W × H, where
The volume of the cone is V = [tex]\frac{1}{3}[/tex] π r² h, where
∵ 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 = [tex]\frac{1}{2}[/tex] diameter = [tex]\frac{1}{2}[/tex] (4)
∴ r = 2 cm
→ Substitute them in the 2nd rule above to find the volume of each cone
∵ V = [tex]\frac{1}{3}[/tex] (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
