Question

a cylindrical sponge cake has a cream - filled middle. what is the volume of the cake part? a) 119 cm³ b) 102 cm³ c) 84 cm³ d) 18 cm³

Explanation:

Step1: Recall volume formula for cylinder

The volume formula for a cylinder is $V = \pi r^{2}h$.

Step2: Calculate volume of outer - cylinder

The outer - radius $R=1.8$ cm and height $h = 10$ cm. So, $V_{outer}=\pi R^{2}h=\pi\times(1.8)^{2}\times10 = 32.4\pi$ cm³.

Step3: Calculate volume of inner - cylinder

The inner - radius $r = 0.75$ cm and height $h = 10$ cm. So, $V_{inner}=\pi r^{2}h=\pi\times(0.75)^{2}\times10=5.625\pi$ cm³.

Step4: Calculate volume of the cake

The volume of the cake $V = V_{outer}-V_{inner}=\pi(32.4 - 5.625)\times10=\pi\times26.775\times10 = 267.75\pi\approx 84$ cm³.

Answer:

c) $84$ cm³