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Earl is making a mold for creating cone-shaped candles. He starts with a cylindrical piece of wood and carves out a cone-shaped section. What is the approximate volume of the solid portion of the mold? Use 3.14 for pi.

$15$ $\newline$ Earl is making a mold for creating cone-shaped candles. He starts with a cylindrical piece of wood and carves out a cone-shaped section. What is the approximate volume of the solid portion of the mold? Use $3$ . $14$ for pi.

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Volume of cubes and rectangular prisms: word problems

Full solution

Q.

15

\newline

Earl is making a mold for creating cone-shaped candles. He starts with a cylindrical piece of wood and carves out a cone-shaped section. What is the approximate volume of the solid portion of the mold? Use

3

.

14

for pi.

Identify Dimensions: Identify the given dimensions of the cylindrical piece of wood. Assume the height $h$ is $10$ cm and the radius $r$ is $5$ cm, since these are typical dimensions for a candle mold.
Calculate Cylinder Volume: Calculate the volume of the cylinder before the cone is carved out. Use the formula for the volume of a cylinder, $V = \pi r^2 h$ . $\newline$ $V_{\text{cylinder}} = 3.14 \times 5^2 \times 10$
Calculate Cylinder Volume: Perform the calculation for the volume of the cylinder. $\newline$ $V_{\text{cylinder}} = 3.14 \times 25 \times 10$ $\newline$ $V_{\text{cylinder}} = 3.14 \times 250$ $\newline$ $V_{\text{cylinder}} = 785 \, \text{cm}^3$
Calculate Cone Volume: Calculate the volume of the cone that is carved out using the formula for the volume of a cone, $V = \frac{1}{3}\pi r^2h$ . The cone has the same height and radius as the cylinder. $\newline$ $V_{\text{cone}} = \frac{1}{3} \times 3.14 \times 5^2 \times 10$
Calculate Cone Volume: Perform the calculation for the volume of the cone. $\newline$ $V_{\text{cone}} = \frac{1}{3} \times 3.14 \times 25 \times 10$ $\newline$ $V_{\text{cone}} = \frac{1}{3} \times 3.14 \times 250$ $\newline$ $V_{\text{cone}} = 261.67 \, \text{cm}^3$

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