MATH SOLVE

2 months ago

Q:
# An open rectangular box with square base has a volume of 256 cubic inches. determine the equation for the volume and surface area of the box.

Accepted Solution

A:

let

b-----------> the length side of the square box

h------------> the height of the box

SA---------> surface area of the box

we know that

[volume of the box]=b²*h

volume=256 in³

b²*h=256-------> h=256/b²-----> equation 1

surface area of the box=area of the base+perimeter of base*height

area of the base=b²

perimeter of the base=4*b

surface area=b²+(4*b)*h------> SA=b²+4*b*h-----> equation 2

substitute equation 1 in equation 2

SA=b²+4*b*[256/b²]-----> SA=b²+1024/b-----> SA=(b³+1024)/b

the answer is

the formula of the volume of the box is V=b²*h-----> 256=b²*h

the formula of the surface area of the box are

SA=b²+4*b*h

SA=(b³+1024)/b

b-----------> the length side of the square box

h------------> the height of the box

SA---------> surface area of the box

we know that

[volume of the box]=b²*h

volume=256 in³

b²*h=256-------> h=256/b²-----> equation 1

surface area of the box=area of the base+perimeter of base*height

area of the base=b²

perimeter of the base=4*b

surface area=b²+(4*b)*h------> SA=b²+4*b*h-----> equation 2

substitute equation 1 in equation 2

SA=b²+4*b*[256/b²]-----> SA=b²+1024/b-----> SA=(b³+1024)/b

the answer is

the formula of the volume of the box is V=b²*h-----> 256=b²*h

the formula of the surface area of the box are

SA=b²+4*b*h

SA=(b³+1024)/b