27. Concrete can be purchased by the cubic yard. How much will it cost to pour a slab 12 feet by 12 feet by 9 inches for a patio if the concrete costs $54.00 per cubic yard? (1 point)
$1,944.00
$972.00
$552.00
$216.00
28. Two square pyramids have the same volume. For the first pyramid, the side length of the base is 14 in., and the height is 24 in. The second pyramid has a height of 96 in. What is the side length of the base of the second pyramid? (1 point)
48 in.
24 in.
12 in.
7 in.
12*12*(9/12) = 108 ft^3
there are 3*3*3 = 27 ft^3/yd^3
108/27 = 4 cubic yards
4*54 = $216
for anything with a pointed top and straight sides the volume =
area of base * height *(1/3)
so here the side^2*h is the same for each
14^2*24 = s^2*96
or
14^2/s^2 = 4
14/s = 2
s = 7
Damon thank you so much god bless you you just saved my life ❤❤❤
You are welcome.
To solve these problems, we need to use the formulas for the volume of a rectangular slab and a square pyramid.
For problem 27, we are given the dimensions of the slab: 12 feet by 12 feet by 9 inches. To find the volume in cubic yards, we need to convert the measurements to yards. Since 1 yard is equal to 3 feet, we can convert the length and width of the slab to yards by dividing them by 3:
Length = 12 feet / 3 = 4 yards
Width = 12 feet / 3 = 4 yards
The height of the slab is given as 9 inches. To convert this to yards, we divide it by 36, since 1 yard is equal to 36 inches:
Height = 9 inches / 36 = 0.25 yards
Next, we calculate the volume of the slab by multiplying the length, width, and height:
Volume = Length x Width x Height = 4 yards x 4 yards x 0.25 yards = 4 cubic yards
Now, we can calculate the cost of the concrete. The cost is given as $54.00 per cubic yard. To find the total cost, we multiply the volume by the cost per cubic yard:
Total Cost = Volume x Cost per cubic yard = 4 cubic yards x $54.00/cubic yard = $216.00
Therefore, the cost to pour the slab for the patio is $216.00 (option D).
For problem 28, we are given the dimensions of two square pyramids. The first pyramid has a side length of 14 in. and a height of 24 in. The second pyramid has a height of 96 in. We need to find the side length of the base of the second pyramid.
The formula for the volume of a square pyramid is given by:
Volume = (1/3) x Base Area x Height
We know that the volume of the two pyramids is the same. The volume of the first pyramid is:
Volume1 = (1/3) x (14 in.)^2 x 24 in. = (1/3) x 196 in.^2 x 24 in. = 196 in.^2 x 8 in. = 1568 in.^3
The volume of the second pyramid is:
Volume2 = (1/3) x Base Area x 96 in.
Since the volumes are equal, we can set up an equation:
Volume1 = Volume2
1568 in.^3 = (1/3) x Base Area x 96 in.
To solve for the base area, we can rearrange the equation:
Base Area = (1568 in.^3) x (3 / 96 in.) = 1568 in.^3 / 32 in. = 49 in.
Therefore, the side length of the base of the second pyramid is the square root of the base area:
Side length of base = √(49 in.) = 7 in.
So, the side length of the base of the second pyramid is 7 inches (option D).