Question

The cone in the diagram has the same height and base area as the prism. What is the ratio of the volume of the come to the volume of the prism?
base area=B
base area =B
volume of cone
volume of prism
1
2
volume of cone
volume of prism
1
3
volume of cone
volume of prism
2
3
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Answer 1

Answer:

$\large\boxed{\dfrac{V_{cone}}{V_{prism}}=\dfrac{1}{3}}$

Step-by-step explanation:

$\text{The formula of a volume of a cone:}\ V_{cone}=\dfrac{1}{3}B_cH_c\\\\B_c-base\ area\ of\ a\ cone\\H_c-height\ of\ a\ cone\\\\\text{The formula of a volume of a prism:}\ V_{prism}=B_pH_p\\\\B_p-base\ area\ of\ a\ prism\\H_p-height\ of\ a\ prism\\\\\text{The cone and the prism have the same base area and height.}\\\text{Therefore}\\\\V_{cone}=\dfrac{1}{3}BH\ \text{and}\ V_{prism}=BH\\\\\text{The ratio of the volume of the cone to the volume of the prism:}$

$\dfrac{V_{cone}}{V_{prism}}=\dfrac{\frac{1}{3}BH}{BH}=\dfrac{1}{3}$