Question

a cylinder and a cone have the same base and height. the cylinder can hold about 4,712 cm³ of sand. jared says that the cone can hold about 1,178 cm³ of sand. which explains whether jared is correct? jared is not correct because the cone and the cylinder have the same base and height so the cone holds 4712/3 ≈ 1571 cm³ of sand. jared is correct because the volume of the cone is less than the volume of the cylinder. the cone holds 4712 - 1178 = 3534 cm³ less sand than the cylinder. jared is correct because the cone and the cylinder have the same base and height so the cone holds 4712/4 = 1178 cm³ of sand. jared is not correct because the volume of the cone cannot be found without knowing the radius of the base and the height of the cone.

Explanation:

Step1: Recall volume formulas

The volume formula for a cylinder is \(V_{cylinder}=\pi r^{2}h\), and for a cone is \(V_{cone}=\frac{1}{3}\pi r^{2}h\). When a cylinder and a cone have the same base (\(r\) is the same) and height (\(h\) is the same), \(V_{cone}=\frac{1}{3}V_{cylinder}\).

Step2: Calculate the volume of the cone

Given \(V_{cylinder} = 4712\mathrm{cm}^{3}\), then \(V_{cone}=\frac{4712}{3}\approx1571\mathrm{cm}^{3}\)

Answer:

Jared is not correct because the cone and the cylinder have the same base and height so the cone holds \(\frac{4712}{3}\approx1571\mathrm{cm}^{3}\) of sand.