Apply the formula V=B×h . What is the volume of a rectangular prism with a length of 1 3/4 in., a width of 4 1/8 in., and a height of 3 2/3 in.? Your answer should be a mixed number in simplest form.
V = B × h
First, calculate the area of the base (B):
B = length × width
B = (1 3/4) in. × (4 1/8) in.
B = (7/4) in. × (33/8) in.
B = 231/32 in²
Now, calculate the volume using the base area and height:
V = (231/32) in.² × (3 2/3) in.
V = (231/32) in.² × (11/3) in.
V = 2541/96 in.³
Convert the improper fraction to a mixed number:
2541 ÷ 96 = 26, with a remainder of 21
V = 26 21/96 in.³
V = 26 7/32 in.³
Therefore, the volume of the rectangular prism is 26 7/32 cubic inches.
wrong
I apologize for the error in the previous calculation. Let's correct it.
Given:
Length = 1 3/4 in. = 7/4 in.
Width = 4 1/8 in. = 33/8 in.
Height = 3 2/3 in. = 11/3 in.
Volume = B × h
Volume = (7/4) in. × (33/8) in. × (11/3) in.
Volume = 231/32 in³ × 11/3
Volume = 2541/96 in³
Divide 2541 by 96:
2541 ÷ 96 = 26 with a remainder of 45
So, in mixed number form, the volume of the rectangular prism is:
26 45/96 in³
Simplify the fraction:
26 45/96 = 26 15/32
Therefore, the volume of the rectangular prism is 26 15/32 cubic inches.