A rectangular box with a square base is 5 times taller than it is wide. If the volume of the box is 6655 cubic centimeters, find the surface area of the box in square centimeters.
The length of a rectangle is 9 more than 4 times its width. The perimeter of the rectangle is 488. Find the length of the rectangle.
The length of a rectangle is 9 more than 4 times its width. The perimeter of the rectangle is 488. Find the length of the rectangle.
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Let sides of rectangular box be L, W, H (Length, width, height)
Since it's a square base, L=W
So volume of rectangular box is L*W*H = 6655cm^3
Or W^2*H =6655cm^3 --> (1)
And given that H = 5*W
Plug that into (1)
W^2*(5W) = 6655cm^3
5W^3 = 6655cm^3
W = 11 cm
H = 5*11 = 55 cm
Surface area of rectangular box = area of square * 2 + area of rectangular sides * 4
=> (11*11*2)+(55*11*4) = 2662 cm^2
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L = 9 + 4W --- (1)
Perimeter = 488 = 2L + 2W
Plug equation (1) into perimeter,
488 = 2(9+4W) + 2W
488 = 18+8W+2W
488 = 18+10W
470 = 10W
W = 47
L = 9 + 4W = 9 + 4(47) = 197
Since it's a square base, L=W
So volume of rectangular box is L*W*H = 6655cm^3
Or W^2*H =6655cm^3 --> (1)
And given that H = 5*W
Plug that into (1)
W^2*(5W) = 6655cm^3
5W^3 = 6655cm^3
W = 11 cm
H = 5*11 = 55 cm
Surface area of rectangular box = area of square * 2 + area of rectangular sides * 4
=> (11*11*2)+(55*11*4) = 2662 cm^2
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L = 9 + 4W --- (1)
Perimeter = 488 = 2L + 2W
Plug equation (1) into perimeter,
488 = 2(9+4W) + 2W
488 = 18+8W+2W
488 = 18+10W
470 = 10W
W = 47
L = 9 + 4W = 9 + 4(47) = 197