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The volume of a prism is the product of its height and area of its base, V = Bh. A rectangular prism has a volume of 16y4 + 16y3 + 48y2 cubic units. Which could be the base area and height of the prism?
a base area of 4y square units and height of 4y2 + 4y + 12 units
a base area of 8y2 square units and height of y2 + 2y + 4 units
a base area of 12y square units and height of 4y2 + 4y + 36 units
a base area of 16y2 square units and height of y2 + y + 3 units
Answers
Given : The volume of a prism is the product of its height and area of its base, V = Bh.
A rectangular prism has a volume of 16y⁴ + 16y³ + 48y² cubic units
To Find : Which could be the base area and height of the prism?
a base area of 4y square units and height of 4y² + 4y + 12 units
a base area of 8y² square units and height of y² + 2y + 4 units
a base area of 12y square units and height of 4y² + 4y + 36 units
a base area of 16y² square units and height of y² + y + 3 units
Solution:
16y⁴ + 16y³ + 48y²
=16y²( y² + y + 3)
Base area of 16y² and height y² + y + 3
Lets check all other options
a base area of 4y square units and height of 4y² + 4y + 12 units
Volume = 4y( 4y² + 4y + 12)
= 16y³ + 16y² + 48y ≠ 16y⁴ + 16y³ + 48y²
a base area of 8y² square units and height of y² + 2y + 4 units
Volume = 8y²( y² + 2y + 4)
= 8y⁴ + 16y³ + 32y² ≠ 16y⁴ + 16y³ + 48y²
a base area of 12y square units and height of 4y² + 4y + 36 units
Volume = 12y( 4y² + 4y + 36)
= 48y³ + 48y² + 432y ≠ 16y⁴ + 16y³ + 48y²
a base area of 16y² square units and height of y² + y + 3 units
16y²( y² + y + 3) = 16y⁴ + 16y³ + 48y²
Hence base area and height of the prism can be
Base area of 16y² and height y² + y + 3
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