An artist makes a sculpture by stacking lanterns on top of one another. Each lantern is a rectangular prism with a length of x inches, a width of (x−3) inches, and a height of 3x inches. If the artist stacks a total of 4 lanterns on top of one another to make the sculpture, which equation represents the volume of the sculpture, V , in cubic inches? Responses V=4x2(x−3) V = 4 x 2 ( x − − 3 ) V=4x2(4x−3) V = 4 x 2 ( 4 x − − 3 ) V=12x2(x−3) V = 12 x 2 ( x − − 3 ) V=12x2(4x−3) V = 12 x 2 ( 4 x − − 3 )An artist makes a sculpture by stacking lanterns on top of one another. Each lantern is a rectangular prism with a length of x inches, a width of (x−3) inches, and a height of 3x inches. If the artist stacks a total of 4 lanterns on top of one another to make the sculpture, which equation represents the volume of the sculpture, V , in cubic inches? Responses V=4x2(x−3) V = 4 x 2 ( x − − 3 ) V=4x2(4x−3) V = 4 x 2 ( 4 x − − 3 ) V=12x2(x−3) V = 12 x 2 ( x − − 3 ) V=12x2(4x−3) V = 12 x 2 ( 4 x − − 3 )

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Respuesta :

anbu40 anbu40 · Answer 1 · 2024-03-05T15:44:03+01:00

Answer:

12x²(x -3)

Step-by-step explanation:

To find the volume of the sculpture, first find the volume of one lantern and then multiply the volume of one lantern by 4.

[tex]\boxed{\bf Volume \ of \ rectangular \ prism = length * width* height}[/tex]

Dimensions of the lantern:

Length = x inches

Width = (x -3) inches

Height = 3x inches

Volume of one lantern = x * (x- 3) * 3x

= 3x²(x -3)

Volume of the sculpture, V = 4 * Volume of one lantern

= 4 * 3x² (x -3)

= 12x²(x - 3)

[tex]\boxed{\bf V = 12x^2(x -3)}[/tex]