Brian needs to start planning for an upcoming move. He is choosing two different size boxes to pack the majority of his stuff. The volume of the first is 1,728 in³ and the second is 13,824 in³. What is the ratio of the surface areas? Given that the boxes are cubes, what is the surface area of the larger of the two boxes?

Solution:

Given,

Volume of the-

First cube box=1728 in³

Second cube box=13824in³

We know that volume of cube =a³

So for the first box

a³= 1728 in³

a= 12 in

Now, surface area of the first box

6a²= 6×(12)²

= 864 in²

and for the second box

b³= 13824 in³

b= 24 in

Now, the surface area of the second box

6b²= 6×(24)²

= 3456 in²

Now, the ratio of the surface area of first box to the second box will be

864:3456

=1:4

The surface area of the larger of two boxes is

3456 in²

the answer is c

hope this !

step-by-step explanation:

we are given a graph for system of inequalities.

in order to write the system of inequalities for the given graph, we need to find the inequality for each of the line separately.

let us find the slope of dotted line first.

taking two coordinates on the graph.

let us say (0,0) and (3,1).

let us find the slope of the line now.

slope of the dotted line would be =.

y-intercept of dotted line is y=0 only.

plugging slope m= and b=0 in slope-intercept form y=mx+b, we get

.

the line is shaded up of that dotted line.

therefore, for shading up we would take greater than inequality symbol > .

and because it's a dotted line we would take only > symbol in place of = sign in above equation of line.

therefore, inequality for dotted line would be

let us take two points (3,1) and (0,4) on the solid line.

slope of the solid line would be =.

for the solid line we have y-intercept b= 4.

plugging slope m= -1 and b=4 in slope-intercept form y=mx+b, we get

y = -1x + 4.

the line is shaded down of that solid line.

therefore, for shading down we would take less than inequality symbol < .

and because it's a solid line we would take ≤ symbol in place of = sign in above equation of line.

therefore, inequality for solid line would be