Question

three students calculated the volume of a cylinder each used a different strategy. for each student, decide if you agree with their strategy explain your reasoning
1 jada said, \i used the formula ( v = bh )\
2 andre said, \i found the area of a circular cross section and multiplied it by the cylinders height\
3 han said, \i used the formula ( v=pi r^{2}h )\

Explanation:

1. Jada's formula \(V = Bh\) is correct. Here, \(B\) represents the area of the base (for a cylinder, the base is a circle). The volume of any prism - like shape (a cylinder is a circular prism) is the area of the base times the height.
2. Andre's strategy is correct. The area of the circular cross - section is the area of the base (\(B=\pi r^{2}\)). And as the volume of a cylinder \(V = Bh\), finding the area of the circular cross - section (base area) and multiplying by the height gives the volume.
3. Han's formula \(V=\pi r^{2}h\) is correct. Since \(B\) (the area of the base, which is a circle) has the formula \(B = \pi r^{2}\), substituting into \(V=Bh\) gives \(V=\pi r^{2}h\).

Answer:

1. Agree. Because for a cylinder (a type of prism - like shape), the volume formula \(V = Bh\) (where \(B\) is the base area) is valid.
2. Agree. The area of the circular cross - section is the base area \(B\) of the cylinder, and \(V = Bh\) (where \(h\) is the height of the cylinder) is the volume formula.
3. Agree. Since the base of a cylinder is a circle with area \(B=\pi r^{2}\), substituting into \(V = Bh\) gives \(V=\pi r^{2}h\).