Question

A rectangular prism has the following dimensions: l = 5a , w = 2a ,

h = ( a³ - 3a² + a ) Use the formula V = l ⋅ w ⋅ h to find the volume of the rectangular prism.

A. 10α⁵ - 3α² + a
B. 10α⁴ - 30α³ + 10α²
C. 10α⁶ - 30α⁴ + 10α²
D. 10α⁵ - 30α⁴ + 10α³

Answer 1

The volume of the rectangular prism is 10a⁵ - 30a⁴ + 10a³.

Step-by-step explanation:

To find the volume of the rectangular prism, we can use the formula V = l ⋅ w ⋅ h where l is the length, w is the width, and h is the height. Given that l = 5a, w = 2a, and h = (a³ - 3a² + a), we can substitute these values into the formula to calculate the volume.

Substituting the values, we have V = (5a) ⋅ (2a) ⋅ (a³ - 3a² + a).

Simplifying further, V = 10a² ⋅ (a³ - 3a² + a) = 10a⁵ - 30a⁴ + 10a³. Therefore, the volume of the rectangular prism is 10a⁵ - 30a⁴ + 10a³.