Question

hatties grandma has baked a cake, as shown in the picture, for hattie and three of her cousins. the cake has a diameter of 9 inches and a height of 4 inches. inside the cake is baked a small marble. hatties grandma slices four pieces of cake, each with an arc length of 3 inches. she says that if hattie or one of her cousins get the marble in their piece of cake, they will get a gift. complete each part of this task to help hattie strategize how best to get the marble. part a what is the volume of the cake? type the correct answer in the box. use numerals instead of words. the volume of the cake is π in³.

Explanation:

Step1: Find the radius of the cake

The diameter of the cake is 9 inches, so the radius $r=\frac{9}{2}= 4.5$ inches.

Step2: Use the formula for the volume of a cylinder

The formula for the volume of a cylinder is $V=\pi r^{2}h$. The height $h = 4$ inches. Substitute $r = 4.5$ and $h=4$ into the formula: $V=\pi\times(4.5)^{2}\times4$.

Step3: Calculate the volume

First, $(4.5)^{2}=20.25$. Then $V=\pi\times20.25\times4=81\pi$.

Answer:

$81$