# The radii of the ends of a frustum of a cone 45cm high are 28cm and 7cm. Find the ratio between the volume of a frustum of a cone and larger cone (given cone). ?

$Consider\;the\;figure\\* \Rightarrow \frac{h}{45}=\frac{28}{7}\Rightarrow h= 45\times 4=180\;cm\\* volume\;of\;frustum\;of\;cone=\frac{1}{3}\times \pi \times 45(28^2+7^2+28\times 7)\\* Volume\;of\;bigger\;cone=\frac{1}{3}\times \pi \times (28)^2\times 180\\* ratio\;of\;volume\;of\;frustum\;of\;one\;and\;bigger\;cone=\\*\Rightarrow \frac{\frac{1}{3}\times \pi \times 45(28^2+7^2+28\times 7)}{\frac{1}{3}\times \pi \times (28)^2\times 180}=\frac{45(784+49+196)}{784\times 180}\\* \Rightarrow \frac{45\times 1029}{784 \times 180}=0.328\approx \frac{1}{3}\\* So,\;the\;ratio\;between\;the\;volume\;of\;a\;frustum\;of\;a\; cone \\*and \;larger \;cone\;1:3$

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