Question

There are two similar cones. Cone A has an altitude of 5 cm and Cone B has analtitude of 13 cm.If Cone A weighs 20 lbs, how much does Cone B weigh?Enter your answer in decimal form. Do not round.

Answer 1

First cone: h=5cm

Second cone: h=13cm

They are similar!

Since they are similar, the radius and height are also similar.

Therefore:

$\frac{h_1}{r_1}=\frac{h_2}{r_2}$

Replacing:

$\begin{gathered} \frac{5}{r_1}=\frac{13}{r_2} \\ r_25=13r_1 \\ r_2=\frac{13}{5}r_1 \end{gathered}$

Now, the volume of a cone is given by:

$\begin{gathered} V_1=\frac{\pi *r_1^2*h_1}{3} \\ V_2=\frac{\pi(r_2)^2h_2}{3} \end{gathered}$

Dividing v1/v2:

$\frac{V_1}{V_2}=\frac{\pi(r_{1})^{2}h_{1}}{3}*\frac{3}{\pi(r_2)^2h_2}$

Solving:

$\frac{V_1}{V_2}=\frac{r_1^2*5}{r_2^2*15}$

Substituing r2=(13/5)* r1

$\frac{V_{1}}{V_{2}}=\frac{r_1^2*5}{(\frac{13}{5})^2*r_1^2*15}$

Simplifying:

$\frac{V_1}{V_2}=\frac{5*5^2}{13^2*15}=\frac{125}{2535}$

We can assign V1=20lb since the volume could represent weight if the material of both cones are uniform:

$\begin{gathered} \frac{20}{V_2}=\frac{125}{2535} \\ V_2=\frac{20*2535}{125}=405.6\text{ }lb \end{gathered}$

The asnwer is: The cone B weigh: 405.6 lb.