Question

show your equations and solutions
find the volume of the composite figure if ( m d = 17 ), ( d v = 85 ),
and ( a d = 20 ). round to the nearest hundredth.

Explanation:

Step1: Identify the composite figure

The composite figure is a combination of a cone and a cylinder. Let's assume \( MN \) is the height of the cone (\( h_{cone} = 17 \)), \( BY \) is the radius (\( r = 8.5 \)), and \( KD \) is the height of the cylinder (\( h_{cylinder}=26 \)).

Step2: Volume of the cone

The formula for the volume of a cone is \( V_{cone}=\frac{1}{3}\pi r^{2}h \).
Substitute \( r = 8.5 \) and \( h = 17 \) into the formula:
\( V_{cone}=\frac{1}{3}\pi(8.5)^{2}(17) \)
\( (8.5)^{2}=72.25 \), so \( V_{cone}=\frac{1}{3}\pi\times72.25\times17 \)
\( \frac{1}{3}\times72.25\times17=\frac{1228.25}{3}\approx409.4167 \)
\( V_{cone}\approx409.4167\pi \)

Step3: Volume of the cylinder

The formula for the volume of a cylinder is \( V_{cylinder}=\pi r^{2}h \).
Substitute \( r = 8.5 \) and \( h = 26 \) into the formula:
\( V_{cylinder}=\pi(8.5)^{2}(26) \)
\( (8.5)^{2}=72.25 \), so \( V_{cylinder}=\pi\times72.25\times26 \)
\( 72.25\times26 = 1878.5 \)
\( V_{cylinder}=1878.5\pi \)

Step4: Total volume of the composite figure

\( V_{total}=V_{cone}+V_{cylinder} \)
\( V_{total}\approx409.4167\pi + 1878.5\pi=(409.4167 + 1878.5)\pi=2287.9167\pi \)
\( \pi\approx3.1416 \), so \( V_{total}\approx2287.9167\times3.1416 \)
\( 2287.9167\times3.1416\approx2287.9167\times3 + 2287.9167\times0.1416 \)
\( 2287.9167\times3 = 6863.7501 \)
\( 2287.9167\times0.1416\approx324.07 \)
\( V_{total}\approx6863.7501+324.07 = 7187.8201\approx7187.82 \) (rounded to the nearest hundredth)

Answer:

The volume of the composite figure is approximately \(\boxed{7187.82}\) (assuming the units are cubic units, and the values of \(MN\), \(BY\), and \(KD\) are in appropriate linear units).