Question

Which of the following formulas could be used to determine the volume of a cone stacked on top of half a sphere? Select all that apply.

- V = lwh
- V = Bh
- V = 1/3 Bh
- V = πr²h
- V = 1/3 πr²h
- V = 4/3 πr³

Answer 1

To find the volume of a cone stacked on top of half a sphere, use
`\(V_{\text{total}} = (1)/(3) \pi r^2 h + (2)/(3) \pi r^3\)`.

To determine the volume of a cone stacked on top of half a sphere, we need to consider the individual volumes of the cone and the hemisphere and then add them together. The formula for the volume of a cone is
`\(V = (1)/(3) \pi r^2 h\)`, where r is the radius of the base and h is the height. The formula for the volume of a hemisphere (half a sphere) is
`\(V = (2)/(3) \pi r^3\)`, where r is the radius.

To find the combined volume, we sum the volumes of the cone and hemisphere:
`\(V_{\text{total}} = V_{\text{cone}} + V_{\text{hemisphere}}\)`. Substituting the respective formulas, we get
`\(V_{\text{total}} = (1)/(3) \pi r^2 h + (2)/(3) \pi r^3\)`.

Among the provided options, the correct formulas for the volume of the described shape are:

1.
`\(V = (1)/(3) \pi r^2 h\)` (for the cone)

2.
`\(V = (2)/(3) \pi r^3\)` (for the hemisphere)

Therefore, the correct combination to determine the total volume is not directly provided in the given options. However, the correct formula for the total volume,
`\(V_{\text{total}}\), is \(V_{\text{total}} = (1)/(3) \pi r^2 h + (2)/(3) \pi r^3\)`.