An open top box with a square base has a volume of 30ft^3. The total surface area of the box is?
a) S.A=x^2-60/x
b) S.A=x^2+60/x
c) S.A=x^2-120/x
d) S.A=x^2+120/x
The base is x^2
The height is 30/x^2
So, the area is x^2 + 4(x)(30/x^2)
To find the surface area of the open top box, we need to calculate the area of each side and then sum them up.
Let's denote the length of one side of the square base as x.
The area of each side of the square base is x^2.
Since the box is open on the top, there are only four sides to consider: the four vertical sides.
The height of the box (which is the same as the height of the vertical sides) can be found by dividing the volume of the box (30 ft^3) by the area of the square base (x^2).
So, the height is 30/x^2.
The area of each vertical side is the product of the height and the length (which is x for each side), giving us a total of 4 * (x * (30/x^2)) = 120/x.
However, we also need to include the surface area of the square base, which is x^2.
So, the total surface area of the box is x^2 + 120/x.
Thus, the correct answer is:
d) S.A=x^2+120/x.
To find the total surface area of the box, we need to find the areas of all the sides and add them together.
Let's call the length of one side of the square base x. Since the base is square, the other side is also x. Therefore, the area of the base is x * x = x^2.
The box has no top, so it only has five sides: the base and the four vertical sides.
The area of each vertical side is found by multiplying the height of the box by the length of the side. The height of the box is determined by the volume, which is given as 30 ft^3. The height can be found by dividing the volume by the area of the base: height = volume / base area = 30 / x^2.
So, the area of each vertical side is (height) * (side length) = (30 / x^2) * x = 30x / x^2 = 30/x.
Since there are four vertical sides, the combined area of the vertical sides is 4 * (30/x) = 120/x.
Adding the area of the base and the combined area of the vertical sides, we get the total surface area:
Total surface area = base area + vertical sides area = x^2 + 120/x.
Therefore, the correct answer is:
d) S.A = x^2 + 120/x.