Question

michael makes his own spice mixes. he uses a funnel to fill his jars of spices. michael’s funnel is shaped like a cone with a height of 2.5 inches and a radius of 2.8 inches. what is the volume of michael’s funnel?
round your answer to the nearest whole number.
cubic inches
michael’s spice jar is shaped like a cylinder with a height of 4 inches and a radius of 0.75 inches. what is the volume of his spice jar?
round your answer to the nearest whole number.
cubic inches
complete the sentence below to describe the relationship between the volumes of the funnel and spice jar. use a whole number.
the volume of the funnel is times the volume of the spice jar.

Explanation:

Step1: Calculate the volume of the cone - shaped funnel

The formula for the volume of a cone is \(V=\frac{1}{3}\pi r^{2}h\). Given \(r = 2.8\) inches and \(h=2.5\) inches.

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Rounding to the nearest whole number, \(V_{funnel}\approx21\) cubic inches.

Step2: Calculate the volume of the cylinder - shaped spice jar

The formula for the volume of a cylinder is \(V=\pi r^{2}h\). Given \(r = 0.75\) inches and \(h = 4\) inches.

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Rounding to the nearest whole number, \(V_{jar}\approx7\) cubic inches.

Step3: Find the relationship between the two volumes

To find how many times the volume of the funnel is the volume of the jar, we calculate \(\frac{V_{funnel}}{V_{jar}}\). \(\frac{21}{7}=3\)

Answer:

21 cubic inches, 7 cubic inches, 3