The Total Surface Area Of Rectangular Solid Is 4.65cm. If The Solid Is 7cm Long And 5cm Wide, Calculate The Height.
2.5cm
let the height be h cm
so 2(7h) + 2(5h) + 2(5)(7) = 4.65 cm^2
14h + 10h + 70 = 4.65
24h = negative
this question is bogus, once you realize that the area of the base alone would be 35 cm^2, without even considering the other surfaces.
How can the total be only 4.65 cm^2
To calculate the height of the rectangular solid, we first need to identify the formula for the total surface area of a rectangular solid. The formula is:
Total Surface Area = 2lw + 2lh + 2wh
where:
l = length
w = width
h = height
Given:
Total Surface Area = 4.65 cm
Length (l) = 7 cm
Width (w) = 5 cm
Since we are calculating the height, we rearrange the formula and isolate the height variable:
Total Surface Area = 2lw + 2lh + 2wh
4.65 cm = 2(7 cm)(5 cm) + 2(7 cm)(h) + 2(5 cm)(h)
4.65 cm = 70 cm^2 + 14h + 10h
Combine the like terms:
4.65 cm = 70 cm^2 + 24h
4.65 cm - 70 cm^2 = 24h
Subtract 70 cm^2 from both sides:
-65.35 cm = 24h
Now divide both sides by 24 to isolate h:
h = -65.35 cm / 24
Calculating this value:
h ≈ -2.72 cm
The height of the rectangular solid, based on the given dimensions and total surface area, is approximately -2.72 cm.
However, it is important to note that dimensions such as length, width, and height cannot be negative in physical objects. Therefore, it seems there may be a mistake in the given information or calculations. Please double-check the values provided for accuracy.