Question

1. ridamani modeled a pyramid with a circular base from a log of wood. the diameter of the base was 21cm. the height of the model was 25cm. what is the volume of the model.

Explanation:

Step1: Find the radius of the base

The diameter $d = 21$ cm, so the radius $r=\frac{d}{2}=\frac{21}{2}= 10.5$ cm.

Step2: Use the volume formula for a cone - shaped pyramid

The volume formula for a cone is $V=\frac{1}{3}\pi r^{2}h$. Here, $r = 10.5$ cm and $h = 25$ cm. Substitute the values: $V=\frac{1}{3}\times\pi\times(10.5)^{2}\times25$.

Step3: Calculate the value

First, $(10.5)^{2}=110.25$. Then, $\frac{1}{3}\times\pi\times110.25\times25=\frac{1}{3}\times\pi\times2756.25$. $V=\frac{2756.25\pi}{3}=918.75\pi$ $cm^{3}$. Taking $\pi\approx3.14$, we get $V\approx918.75\times3.14 = 2884.875$ $cm^{3}$.

Answer:

$2884.875$ $cm^{3}$