The dimensions of a pyramid are increased by 1100%. The percentage increase in surface area is
The new dimensions are ___times the original dimensions, and the new surface area is ___times the original surface area. The increase in surface area is___%.
(answer explained)
1110% = dimensions x 12
12^2= 144
x 1444 original surface area
% increase = 144-1/1 x 100
=14300
Therefore the surface area is 14300% larger
12, 144, 14300%
Well, well, well, looks like our pyramid is growing bigger! If the dimensions of the pyramid are increased by a whopping 1100%, that means they become 12 times their original size. Yes, 12!
Now, let's talk about the surface area. The surface area of a pyramid is directly proportional to the square of the dimensions. So, if the dimensions are increased by 12 times, the surface area will be increased by a squaring of that, which is 144 times the original surface area. Woah!
So, the new dimensions are 12 times the original dimensions, and the new surface area is 144 times the original surface area. That's quite a significant increase, if you ask me.
To calculate the percentage increase in surface area, we just need to take the new surface area, subtract the original surface area from it, divide by the original surface area, and finally multiply by 100.
So, let's do the math: (144 - 1) / 1 * 100 = 14300%
That's right, the increase in surface area is a whopping 14300%. Looks like our pyramid has really gotten the expansion bug!
To calculate the percentage increase in surface area of a pyramid when its dimensions are increased by 1100%, we need to consider the formula for the surface area of a pyramid.
The surface area of a pyramid is given by the formula:
S = (base area) + (side area)
The base area is calculated by:
Base area = length × width
And the side area is calculated by:
Side area = (1/2) × perimeter × slant height
Now, let's assume that the original dimensions of the pyramid are x and y (length and width, respectively).
The new dimensions after a 1100% increase would be:
New length = x + 1100%x = (x + 11x) = 12x
New width = y + 1100%y = (y + 11y) = 12y
So, the new dimensions are 12x times the original length and 12y times the original width.
To calculate the increase in surface area, we need to compare the original surface area (S1) with the new surface area (S2).
Original base area = x × y
Original side area = (1/2) × perimeter × slant height (using Pythagorean theorem)
New base area = 12x × 12y
New side area = (1/2) × perimeter × slant height (using Pythagorean theorem)
Now, let's calculate the percentage increase in surface area:
Increase in surface area = (S2 - S1)
Percentage increase in surface area = (increase in surface area / original surface area) × 100
Note: Since specific values for x, y, and the slant height are not provided, we can only provide the general formula for calculating the percentage increase.
To find the percentage increase in surface area, we need to calculate the new dimensions and the new surface area.
Let's assume the original dimensions of the pyramid are:
Length = L,
Width = W,
Height = H.
If the dimensions are increased by 1100%, we need to add 1100% of each dimension to itself.
This can be calculated as follows:
New Length = L + (1100/100) * L = L + 11L = 12L
New Width = W + (1100/100) * W = W + 11W = 12W
New Height = H + (1100/100) * H = H + 11H = 12H
Now let's find the new surface area of the pyramid.
The surface area formula for a pyramid is:
Surface Area = (Length * Width) + (Length * √(Width/2)^2 + Height^2) + (Width * √(Length/2)^2 + Height^2)
Original Surface Area = (L * W) + (L * √(W/2)^2 + H^2) + (W * √(L/2)^2 + H^2)
New Surface Area = (12L * 12W) + (12L * √(12W/2)^2 + (12H^2) + (12W * √(12L/2)^2 + 12H^2)
Now we can calculate the percentage increase in surface area:
Percentage Increase = (New Surface Area - Original Surface Area) / Original Surface Area * 100
Please provide the original dimensions (L, W, H) of the pyramid, and we can substitute them into the formulas above to calculate the actual percentage increase in surface area.