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A cone has a volume of
365mm^(3). If a scale factor of 0.5 were applied to the cone, what would its new volume be?

A cone has a volume of $365 \mathrm{~mm}^{3}$ . If a scale factor of $0$ . $5$ were applied to the cone, what would its new volume be?

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Scale drawings: word problems

Full solution

Q. A cone has a volume of

365 \mathrm{~mm}^{3}

. If a scale factor of

0

.

5

were applied to the cone, what would its new volume be?

Understand Relationship Scale Factor Volume: Understand the relationship between the scale factor and the volume of the cone. $\newline$ When a scale factor is applied to a three-dimensional object, the new volume is the cube of the scale factor times the original volume. This is because volume is a three-dimensional measure, and scaling an object affects its length, width, and height.
Apply Scale Factor Find Volume: Apply the scale factor to the original volume to find the new volume. $\newline$ The scale factor is $0.5$ , so we need to cube this scale factor to apply it to the volume. $\newline$ New Volume = (Scale Factor) $^3$ * Original Volume $\newline$ New Volume = $(0.5)^3 * 365 \, \text{mm}^3$
Calculate New Volume: Calculate the new volume. $\newline$ New Volume = $(0.5 \times 0.5 \times 0.5) \times 365 \, \text{mm}^3$ $\newline$ New Volume = $(0.125) \times 365 \, \text{mm}^3$ $\newline$ New Volume = $45.625 \, \text{mm}^3$ $\newline$ Since volume is typically rounded to the nearest whole number, we can round this to $46 \, \text{mm}^3$ .

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