The diameter of the base of a cone is 8 inches and the height is twice the radius. What is the volume of the cone? Use 3.14 for \( \pi \). \( 401.92 \mathrm{in}^{3} \) \( 133.97 \mathrm{in}^{3} \) \( 50.24 \mathrm{in}^{3} \) \( 66.99 \mathrm{in}^{3} \)

To find the volume of the cone, you can use the formula \( V = \frac{1}{3} \pi r^2 h \). The diameter of the base is 8 inches, so the radius \( r \) is 4 inches. Given that the height \( h \) is twice the radius, the height is \( 2 \times 4 = 8 \) inches. Now, substituting these values into the formula: \[ V = \frac{1}{3} \times 3.14 \times (4)^2 \times 8 = \frac{1}{3} \times 3.14 \times 16 \times 8 = \frac{1}{3} \times 3.14 \times 128 \approx 134.04 \, \mathrm{in}^{3}. \] Thus, the closest option is \( 133.97 \mathrm{in}^{3} \). When working with geometry, it’s handy to remember the basic properties of 3D shapes. A cone's volume is directly influenced by its base area and height. So, if you ever need to upscale a cone, you mainly need to know how changing the base or height will impact the volume! Also, remember to always check your units, especially with problems involving volume. In this case, make sure you’re consistently using inches or converting them to a different unit before calculating. Being careful with unit conversions can save you from those pesky miscalculations!