ACT Math · Linear equations and inequalities

The formula for the volume of a cone is V = 1/3π r² h. Which equation correctly solves for h?

The formula for the volume of a cone is V=13πr2hV = \dfrac{1}{3}\pi r^2 h. Which equation correctly solves for hh?

Answer and explanation

Answer: C: h = (3V)/(π r²)

Start with V=13πr2hV=\frac{1}{3}\pi r^2h. Multiply both sides by 33 to remove the fraction: 3V=πr2h3V=\pi r^2h. Then divide both sides by πr2\pi r^2: h=3Vπr2h=\frac{3V}{\pi r^2}, choice C. Choice B (V3πr2\frac{V}{3\pi r^2}) leaves the 33 in the denominator, though it should multiply VV. Choice A (3Vπr23V\pi r^2) multiplies by πr2\pi r^2 rather than dividing. Choice D (πr23V\frac{\pi r^2}{3V}) is the reciprocal of the correct answer. A good check is to substitute h=3Vπr2h=\frac{3V}{\pi r^2} back into the formula, which gives VV.

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