Question

what is the volume of this cone?
round your answer to the nearest hundredth.
16.3 in
30.4 in
cubic inches

Explanation:

Step1: 求圆锥底面半径

圆锥底面直径\(d = 30.4\)英寸，根据\(r=\frac{d}{2}\)，可得底面半径\(r=\frac{30.4}{2}=15.2\)英寸。

Step2: 求圆锥的高

根据勾股定理\(h=\sqrt{l^{2}-r^{2}}\)（\(l\)为圆锥母线长，\(l = 16.3\)英寸），则\(h=\sqrt{16.3^{2}-15.2^{2}}=\sqrt{(16.3 + 15.2)(16.3 - 15.2)}=\sqrt{31.5\times1.1}=\sqrt{34.65}\approx5.89\)英寸。

Step3: 计算圆锥体积

圆锥体积公式\(V=\frac{1}{3}\pi r^{2}h\)，将\(r = 15.2\)，\(h\approx5.89\)代入公式，\(V=\frac{1}{3}\times\pi\times15.2^{2}\times5.89=\frac{1}{3}\times\pi\times231.04\times5.89=\frac{1}{3}\times\pi\times1360.8256\approx1424.89\)立方英寸。

Answer:

\(1424.89\)