Question

write which solid has a greater volume: cone with a base radius of 7 centimeters and a height of 28 centimeters or a pyramid with base area of 154 square centimeters and height of 28 centimeters? explain your reasoning. the cone and pyramid have nearly the same volumes. cone: the area of the base is approximately 154 square centimeters, so v ≈ 1/3(154)(28) or about 1437 cubic centimeters. the volume of the pyramid is such a large amount that we can say that the volume of the cone is greater.

Explanation:

Step1: Calculate the base - area of the cone

The formula for the area of the base of a cone (a circle) is $A=\pi r^{2}$. Given $r = 7$ cm, $A=\pi\times7^{2}=49\pi\approx49\times3.14 = 153.86\approx154$ square centimeters.

Step2: Calculate the volume of the cone

The volume formula of a cone is $V_{cone}=\frac{1}{3}Ah$, where $A$ is the base - area and $h$ is the height. Substituting $A\approx154$ square centimeters and $h = 28$ cm, we get $V_{cone}=\frac{1}{3}\times154\times28=\frac{4312}{3}\approx1437$ cubic centimeters.

Step3: Calculate the volume of the pyramid

The volume formula of a pyramid is $V_{pyramid}=\frac{1}{3}Ah$, where $A$ is the base - area and $h$ is the height. Given $A = 154$ square centimeters and $h = 28$ cm, $V_{pyramid}=\frac{1}{3}\times154\times28=\frac{4312}{3}\approx1437$ cubic centimeters.

Answer:

The cone and pyramid have nearly the same volumes. Cone: The area of the base is approximately 154 square centimeters, so $V\approx\frac{1}{3}(154)(28)$ or about 1437 cubic centimeters. The volume of the pyramid is $\frac{1}{3}(154)(28)$ or about 1437 cubic centimeters. We can say that the volumes are approximately equal.