Question

The solids shown have the same base area and height. If the cone is filled with water and poured into the cylinder, how many cones filled with water would it take to fill the cylinder? $\begin{array}{ll}\text { A. } 2 \frac{2}{3} & \text { C. } 3 \frac{1}{3} \\ \text { B. } 3 & \text { D. } 3 \frac{2}{3}\end{array}$

Name: Problem 41, Chapter 11: Prealgebra
Uploaded: 2020-05-18T13:44:09-08:00
Duration: 1 min 33 s
Channel: Sarah Vo
Description: The solids shown have the same base area and height. If the cone is filled with water and poured into the cylinder, how many cones filled with water would it take to fill the cylinder? A. 2 (2)/(3) C. 3 (1)/(3) B. 3 D. 3 (2)/(3)

   The solids shown have the same base area and height. If the cone is filled with water and poured into the cylinder, how many cones filled with water would it take to fill the cylinder?
$\begin{array}{ll}\text { A. } 2 \frac{2}{3} & \text { C. } 3 \frac{1}{3} \\ \text { B. } 3 & \text { D. } 3 \frac{2}{3}\end{array}$

Prealgebra

Carol E. Malloy,… 1st Edition

Chapter 11, Problem 41

Instant Answer

Solved by Expert Sarah Vo

05/18/2020

Step 1

Step 1: The volume of a cylinder is given by the formula $V_{cylinder} = \pi r^2 h$ and the volume of a cone is given by the formula $V_{cone} = \frac{1}{3} \pi r^2 h$. Show more…

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The solids shown have the same base area and height. If the cone is filled with water and poured into the cylinder, how many cones filled with water would it take to fill the cylinder? $\begin{array}{ll}\text { A. } 2 \frac{2}{3} & \text { C. } 3 \frac{1}{3} \\ \text { B. } 3 & \text { D. } 3 \frac{2}{3}\end{array}$

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Key Concepts

Volume of a Cone

The volume of a cone is calculated using the formula V = (1/3) * Base Area * Height. This formula shows that a cone occupies one third of the volume of a cylinder with the same base area and height, providing a fundamental understanding of how the cone's structure affects its storage capacity compared to other solids.

Volume of a Cylinder

The volume of a cylinder is determined by the formula V = Base Area * Height. This linear relationship is direct and emphasizes that for solids sharing the same base and height, a cylinder will always have three times the volume of a cone.

Volume Ratio and Comparison in Solids

When comparing solids with identical base areas and heights, the relationship between their volumes is particularly clear. Since a cone has one third the volume of a cylinder, it takes exactly three such cones to fill a cylinder. This concept is crucial in problems involving volume transfers between different geometric shapes.

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