find the volume of these rectangular prisms
base area:56 square in.
height:5 in.
base area:72 square yards
height:8 yds
Volume = base area * height
To find the volume of a rectangular prism, you need to multiply the base area (length x width) by the height.
For the first rectangular prism:
Base area: 56 square in.
Height: 5 in.
Step 1: Determine the length and width by considering the factors of the base area. Since the base area is 56 square in., you can break it down into pairs of factors: 1 x 56, 2 x 28, 4 x 14, and 7 x 8. These pairs represent the possible length and width combinations.
Step 2: Choose the appropriate length and width combination for the base area, keeping in mind that the length and width must multiply to give the base area of 56 square inches.
Possible combinations:
Length = 7 in. and width = 8 in.
Length = 8 in. and width = 7 in.
Step 3: Multiply the length and width by the height (5 in) to find the volume.
Volume = Length x Width x Height
Volume = (7 in. x 8 in. x 5 in.) or (8 in. x 7 in. x 5 in.)
Volume = 280 cubic inches
For the second rectangular prism:
Base area: 72 square yards
Height: 8 yds
Step 1: Determine the length and width by considering the factors of the base area. Since the base area is 72 square yards, you can break it down into pairs of factors: 1 x 72, 2 x 36, 3 x 24, 4 x 18, 6 x 12, and 8 x 9. These pairs represent the possible length and width combinations.
Step 2: Choose the appropriate length and width combination for the base area, keeping in mind that the length and width must multiply to give the base area of 72 square yards.
Possible combinations:
Length = 8 yds and width = 9 yds.
Length = 9 yds and width = 8 yds.
Step 3: Multiply the length and width by the height (8 yds) to find the volume.
Volume = Length x Width x Height
Volume = (8 yds x 9 yds x 8 yds) or (9 yds x 8 yds x 8 yds)
Volume = 576 cubic yards