Question

clare has a decorative cylindrical vase in her bedroom. the vase has a diameter of 3 inches and a height of 6 inches. clare wants to get a smaller vase for her office. select the vases that have a smaller volume than the one clare currently has. a vase shaped like a cone with a diameter of 3 inches and a height of 6 inches. a vase shaped like cylinder with a radius of 2 inches and a height of 6 inches. a vase shaped like a cone with a radius of 2 inches and a height of 18 inches. a vase shaped like a sphere with a diameter of 3 inches.

Explanation:

Step1: 计算Clare现有圆柱花瓶体积

圆柱体积公式\(V = \pi r^{2}h\)，已知直径\(d = 3\)英寸，则半径\(r=\frac{d}{2}=\frac{3}{2}\)英寸，高\(h = 6\)英寸。
\(V_{1}=\pi\times(\frac{3}{2})^{2}\times6=\pi\times\frac{9}{4}\times6=\frac{27}{2}\pi\approx42.41\)（立方英寸）

Step2: 计算选项A圆锥花瓶体积

圆锥体积公式\(V=\frac{1}{3}\pi r^{2}h\)，直径\(d = 3\)英寸，半径\(r=\frac{3}{2}\)英寸，高\(h = 6\)英寸。
\(V_{A}=\frac{1}{3}\pi\times(\frac{3}{2})^{2}\times6=\frac{1}{3}\pi\times\frac{9}{4}\times6=\frac{9}{2}\pi\approx14.14\)（立方英寸）

Step3: 计算选项B圆柱花瓶体积

圆柱体积公式\(V = \pi r^{2}h\)，半径\(r = 2\)英寸，高\(h = 6\)英寸。
\(V_{B}=\pi\times2^{2}\times6=24\pi\approx75.40\)（立方英寸）

Step4: 计算选项C圆锥花瓶体积

圆锥体积公式\(V=\frac{1}{3}\pi r^{2}h\)，半径\(r = 2\)英寸，高\(h = 18\)英寸。
\(V_{C}=\frac{1}{3}\pi\times2^{2}\times18=\frac{1}{3}\pi\times4\times18 = 24\pi\approx75.40\)（立方英寸）

Step5: 计算选项D球形花瓶体积

球体积公式\(V=\frac{4}{3}\pi r^{3}\)，直径\(d = 3\)英寸，半径\(r=\frac{3}{2}\)英寸。
\(V_{D}=\frac{4}{3}\pi\times(\frac{3}{2})^{3}=\frac{4}{3}\pi\times\frac{27}{8}=\frac{9}{2}\pi\approx14.14\)（立方英寸）

Answer:

A. A vase shaped like a cone with a diameter of 3 inches and a height of 6 inches.
D. A vase shaped like a sphere with a diameter of 3 inches.