A diamensions of a cuboid are in the ratio 4:3:1 and its total surface area is 950cm2 find the diamensions
a = 2(4x*3x+4x*1x+3x*1x) = 38x = 950
x = 25
dimensions are 100 x 75 x 25
drat those disappearing exponents.
for that ratio
the sides would be 4x, 3x, and x
SA = 2(12x^2 + 3x^2 + 4x^2) = 950
38x^2 = 950
x^2 = 25
x = 5
sides are 20, 15 , and 5
check:
SA = 2(20x15) + 2(20x5) + 2(15x5) = 950
good catch. Usually I check my answers.
gotta love that hubris.
To find the dimensions of the cuboid, we need to determine the lengths of all three sides.
Let's assume the dimensions of the cuboid are 4x, 3x, and x, where x is a common factor.
The total surface area of a cuboid can be calculated using the formula: SA = 2lw + 2lh + 2wh, where l, w, and h are the lengths of the sides.
Given that the total surface area is 950 cm², we can set up the following equation:
2(4x*3x) + 2(4x*x) + 2(3x*x) = 950
Simplifying this equation:
24x² + 8x² + 6x² = 950
38x² = 950
Divide both sides by 38 to solve for x:
x² = 25
Taking the square root of both sides:
x = 5
Now, substitute the value of x back into the dimensions of the cuboid:
Length = 4x = 4 * 5 = 20 cm
Width = 3x = 3 * 5 = 15 cm
Height = x = 5 cm
Therefore, the dimensions of the cuboid are 20 cm, 15 cm, and 5 cm.