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Current time:0:00Total duration:3:24

Video transcript

the surface area of a cube is equal to the sum of the areas of its six sides let's just visualize that I like to visualize things so if that's the cube that's the cube we can see three sides three sides are facing us but then if it was transparent we see that there are actually six sides of a cube so there's this one one two three in front and then one this is the bottom this is in the back and this is also in the back so you have three sides of the cube so I believe what they're saying the surface area of a cube with side length X so if this is X if this is X if this is X is given by the expression 6x squared that also makes sense the area of each side is going to be x times X is x squared and there's six of them so it's going to be 6x squared Joline has two cubed shaped containers that you wants to paint one cube has side length too so this is one cube right over here I'm going to my best to draw it so this right over here has side length too so that's its dimensions the other cube has side length 1.5 so the other cube is going to be a little bit smaller it has side length 1.5 so it's one point five by one point five by one point one point five what is the total surface area that she has to paint well we know that the surface area of each cube is going to be six x squared where X is the dimensions of that cube so the surface area of this cube right over here is going to be six and now let me do it in that color of that cube it's going to be six times X where X is the dimensions of the cube and the cube all has the same dimensions or its length width and depth is all the same so for this cube the surface area is going to be six times two squared so it's going to be six times two squared and then the surface area of this cube is going to be is going to be six times 1.5 squared one point five squared and if we want the total surface here she has to paint it's going to be the sum of the two oops so we're just going to add these two things and so if we were to compute this first one right over here this is going to be 6 times 4 this is 24 and this one right over here this is going to be a little bit here here let's see 15 times 15 is 225 so 1.5 times 1.5 is 2.25 so this is going to be so 1.5 squared is two point two five and two point two five times six so let me just multiply that out 2.25 times 6 let's see we're going to have 6 times 5 is 30 6 times 2 is 12 plus 3 is 15 6 times 2 is 12 plus 1 is 13 I have two numbers behind the decimal 13.5 so it's going to be 13.5 and if I add these two together this is going to be equal to the total surface area that she has got to paint is going to be 37 point 5 square well I guess they're not giving us the unit's well 37 point 5 is good the total area square units or whatever the unit's happen to be