Answer:
12πx⁴, 15x⁷, 16x⁹
Explanation:
Volume of a cylinder: πr²h
Volume of a rectangular prism: whl
Plugging in variables for the volume of a cylinder, we get: 3x²·(2x)²·π
3x²·(2x)² = 3·2·2·x·x·x·x
= 12·x⁴
=12x⁴
Now, we just multiply that by π.
12x⁴·π = 12x⁴π
A monomial is a 1-term polynomial, so 12x⁴π is a monomial.
Plugging in variables for the volume of a rectangular prism, we get: 5x³·3x²·x²
5x³·3x² = 5·3·x·x·x·x·x
= 15·x⁵
= 15x⁵
Now, we just multiply that by x².
15x⁵·x²
= 15·x·x·x·x·x·x·x
= 15·x⁷
=15x⁷
A monomial is a 1-term polynomial, so 15x⁷ is a monomial.
Same steps for the last shape, another rectangular prism:
2x²·2x³·4x⁴
2x²·2x³
= 2·2·x·x·x·x·x
= 4·x⁵
= 4x⁵
Now, we just multiply that by 4x⁴.
4x⁵·4x⁴
= 4·4·x·x·x·x·x·x·x·x·x·
= 16·x⁹
= 16x⁹
A monomial is a 1-term polynomial, so 16x⁹ is a monomial.