Question

2 points 2. How do the volumes of the two figures compare? Select all that are correct. 2.5 ft A 2.5 ft-> B 5 ft 3 ft K 3 ft 5 ft Volume A = Volume B Volume A = 0.5Volume B Volume A is greater than Volume B Volume B is greater than Volume A

Answer 1

Given data:

The volume of the triangular prism(A) is,

`\begin{gathered} V=(1)/(2)(3\text{ ft)(2.5 ft)}(5\text{ ft)} \\ =18.75ft^3 \end{gathered}`

The volume of Bis,

`\begin{gathered} V^(\prime)=(5\text{ ft)(3 ft)(2.5 ft)} \\ =37.5ft^3 \end{gathered}`

The ratio of the volume of the prism to the volume of the cuboid is,

`\begin{gathered} \frac{V^{}}{V^(\prime)}=(18.75)/(37.5) \\ (V)/(V^(\prime))=(1)/(2) \\ V=0.5V^(\prime) \end{gathered}`

Thus, volume of B is greater than A , so the second and fourth options are correct.