Question

Isabella was building towers with her little sister.Her little sister has wood piece building blocks of different figures.Isabella places a cone on top of a cylinder to create a tower.She starts to imagine if this figure was large how much space would be inside it.She draws a model of the figure on a piece of paper and starts to find the volume.While the building blocks are not measured in yards her diagram was labeled in yards.Here is her diagram, calculate the volume for Isabella.

Answer 1

Data input

hc = Cone height

hd = cylinder height

r = radius

r= 11/2 = 6.5 yd

hc = 9 yd

hd = 13 yd

Procedure

First we will calculate the volume of the cylinder

$\begin{gathered} V=h_d\cdot\pi\cdot r^2 \\ V=13\cdot\pi\cdot6.5^2 \\ V=1724.64\text{ yd}^3 \end{gathered}$

Second we will calculate the volume of the cone

$\begin{gathered} V=\frac{1}{3}\pi\cdot r^2\cdot h \\ V=\frac{1}{3}\cdot\pi\cdot(6.5)^2\cdot9 \\ V=397.99 \end{gathered}$

The total volume would be the sum of the two volumes calculated above.

$\begin{gathered} Vt=1724.64+397.99 \\ Vt=2122.63 \end{gathered}$

Total volume equals 2122.63 yd^3