Question

what is the volume of the composite figure? use 3.14 for \\(\pi\\) and round the answer to the nearest tenth of a cubic unit.\
\\(\bigcirc\\) 753.6 in.\\(^3\\)\
\\(\bigcirc\\) 904.3 in.\\(^3\\)\
\\(\bigcirc\\) 1,582.6 in.\\(^3\\)\
\\(\bigcirc\\) 1,997.0 in.\\(^3\\)

Explanation:

Step1: Find radius of base

The diameter is 12, so radius $r = \frac{12}{2} = 6$

Step2: Calculate height of cone

Total height is 20, cylinder height is 11. Cone height $h_{cone} = 20 - 11 = 9$

Step3: Volume of cylinder

Use formula $V_{cyl} = \pi r^2 h_{cyl}$
$V_{cyl} = 3.14 \times 6^2 \times 11 = 3.14 \times 36 \times 11 = 1243.44$

Step4: Volume of cone

Use formula $V_{cone} = \frac{1}{3} \pi r^2 h_{cone}$
$V_{cone} = \frac{1}{3} \times 3.14 \times 6^2 \times 9 = \frac{1}{3} \times 3.14 \times 36 \times 9 = 339.12$

Step5: Total volume of composite figure

Add cylinder and cone volumes: $V_{total} = 1243.44 + 339.12 = 1582.56$

Step6: Round to nearest tenth

$1582.56 \approx 1582.6$

Answer:

1,582.6 in.$^3$