A Square Pyramid has a Total Surface Area of 40square inches and the side length of its square base
is 4 inches. Determine the slant height of the
pyramid.
Answers
Answer:
Step-by-step explanation:
Let h be the slant height of the square pyramid.
Given:
Total surface area of the square pyramid = 40 square inches
And square base has a side length = 4 inches
We need to find slant height of the square pyramid.
The surface area of the pyramid is sum of the area of the square and area of each of the triangle faces.
-------(1)
The base area of the square pyramid =
So,
And area of the triangle =
Where b = base of the triangle
The base of the triangle is one side of the square pyramid base, so the base of the triangle is 4 inches.
And h = slant height of the triangle.
So the area of the triangle = 2h square inches
Now we substitute area of the base and area of the triangle in equation 1.
Now we substitute the value of total surface area of the square pyramid in above equation.
Simplify the above equation.
Therefore the slant height of the square pyramid is 3 inches.
Answer:
Step-by-step explanation:
1. 9 square inches
2. 60 square inches
3. 69 square inches
Related Questions
Set up and solve a percent proportion. a) What is 10% of 70?
Plz help, I need answers to these questions ASAP, would appreciate a short step-by-step explanation with each! WILL MARK BRAINLIEST!!!You’ve been given $500.00 for your fencing. So first we are going to make as big of a rectangular field as we can with the money that we have for the fencing to surround it. The cost of premium fencing (only the best for your farm, of course) is $11.41 per metre. So with that, and the following equations:A=l*wP=2l+2wWhere A is the area, P is the perimeter, l is the length, and w is the width of a rectangle, we can find the maximum area that we can have for this field.Perimeter of fence:Area of farm:Let’s say we have access to planting 2 different crops, Watermelons and Grapes. We can find the revenue of a crop by the equation:R = (p0 + px)(n0 - nx)Where R is the revenue, p0 is the starting price, n0 is the amount sold at the starting price, p is the price increase, n is the decrease in the amount sold per price increase, and x is the number of price increases.Crop A: Watermelons have a starting price of $12.00 per m2 of area sold. At this price, you can sell 45 m2 worth. For every $2.00 increase, you will sell 1 m2 less. So the first task is to figure out how to put these values into the equation above and turn it into a quadratic function. Then you will need to find the value of x to make the revenue as large as possible. Once you know x, the number of price increases, you can then find what you should price your Watermelons per m2.Equation: R =Number of price increases: x =Price of Watermelon per m^2 =Okay, now we can do the same thing with the grapes, just to give you that extra practice with quadratic functions. The starting price of grapes per m² is $8.00, at which you can sell 60 m² worth. For every $3.00 increase in price, you sell 3 m² less. So use the same method you just used to find the price of grapes per m² of area to maximize revenue.Equation: R =Number of price increases: x =Price of grape per m^2 =Okay, so now, all in all, we have built our farm and found what to price each of our crops at. Now let’s find what amount of each crop to grow and find our profits. Getting right into it, we have the following cost equations:CW = $20.00 * W + $50.00CG = $10.00 * G + $40.00Where CW is the total cost of planting and growing Watermelons, CG is the total cost of planting and growing Grapes, W is the area of Watermelons planted, and G is the area of Grapes planted. Now that we know our cost, we can finally find our profits. Profit is equal to the price per unit area, multiplied by the area sold, subtracted by the total cost planting and growing them, or, Profit = Price * Area - Cost. But at this point, we still don’t know the area of each crop in our field. But we do know a couple of things to figure it out. We know the total area of our farm, found in the first part. Which we can say is, Area = G + W And we were also only given $1590 to plant the crops. So, $1590.00= CW+CG I’ll help you simplify this a bit:$1590.00=$20.00*W+$50.00+$10.00*G+$40.00 $1590.00=$20.00*W+$10.00*G+$90.00So now we have enough information to solve for the areas of Watermelons and Grapes in your field. Here’s some room to do that. Hint: Use either substitution or graph the two equations to find an intersection.Area of watermelon to plant:Area of grapes to pant:Profit of the crops:
Janelle can get a 24-pack of bottled water for $6.80. How much would Janelle have to pay for a 12-pack of bottled water if the ratios are proportional?
Mia climbs 5/8 of the height of the rock wall. Lee climbs 4/5 of Mia's distance. What fraction of the wall does climb? Show work
Answers
so x = 40/0.08
x = 500
40 is 8% of 500
0.08 × 100 = 8%
40 is 8% of what?
40 = 0.08x
8 and 8 cancels out
x = 500
check
500 × 0.08 = 40
-48
3
-3
Answers
Once you simplify the expression, you will get -24/8
24/8 is 3 and you take the sign of the larger number which is negative
so your answer is (-3)
Hope i helped
Answers
Answers
Answer: 176m
Step-by-step explanation:
First we have to convert the meters in the scale to millimeters
4m = 4*1000mm
Now we got the scale 11:4000
11x = 4000 * 484
x= (4000*484)/11
x = 4000 * 44
x = 176000mm = 176m
Ex: In the drawing 484 millimeters so 44x11 millimeters: 176
Answers