Question

The dimensions of a storage container in the shape of a rectangular prism are 54 in x 32.25 in x 24.5 in. Choose True or False for each statement

The most precise dimension has 4 significant digits.

Written using the correct number of significant digits, the volume of the container has 3 significant digits

Written using the correct number of significant digits,the surface area of the container is rounded to the ones place

Answer 1

GIVEN

the dimensions ofrectangular prism are

length = 54 in

breadth = 32.25in

height = 24.5 in

formula

volume of the rectangular prism = length×breadth×height

= 54 ×32.25×24.5

= 42997.5 in³

first statement is false because the volume of the rectangular prism in two significant digit.

Second statement is false because the volume of the rectangular prism in two significant digit.

FORMULA

surface area of a rectangular prism = 2(wl+hl+hw)

by putting the value of the length , breadth & height

we get

= 2 (54×32.25 + 32.25×24.5 + 24.5×54)

= 7709.25 in²

= 7709.3 in²(approx)

Third statement is true the surface area of the container is rounded to ones place.

Hence proved

Answer 2

Statement 1 is false.

Statement 2 is false.

Statement 3 is true.

Explanation:

Given : The dimensions of a storage container in the shape of a rectangular prism are 54 in × 32.25 in × 24.5 in.

To find : Choose True or False for each statement.

Solution :

The dimensions of a rectangular prism are 54 in × 32.25 in × 24.5 in.

Statement 1 - The most precise dimension has 4 significant digits.

The most precise dimension is 54 and it has two significant digits.

So, Statement 1 is false.

Statement 2 - Written using the correct number of significant digits, the volume of the container has 3 significant digits.

The volume of the container,

`V=l* b* h`

`V=54*32.25* 24.5`

`V=42666.75\ in^3`

The volume of the container is not having 3 significant digits.

So, Statement 2 is false.

Statement 3 - Written using the correct number of significant digits,the surface area of the container is rounded to the ones place.

The surface area of the container,

`S=2(lb+ bh+ hl)`

`S=2((54)(32.25)+(32.25)(24.5)+(24.5)(32.25))`

`S=2(1741.5+790.125+790.125)`

`S=2(3321.75)`

`S=6643.5\ in^2`

So, Statement 3 is true the surface area of the container is rounded to ones place.