In math what is the answer to this question. -27•7/9=

Evelyn's made a cake in the shape of a circus tent the cake consisted of a cylinder and a cone .The height of the cone is half t

Lera25 [3.4K]

The volume of the cake is 1470 in³.
volume of a cylinder = πr² x height
(Think about how a cylinder is basically a bunch of circles stacked on top of each other. To find the volume, first you need the area of the circle (πr², then you multiply by how many circles you are stacking on top of each other (height))

we know the diameter of the cylinder is 12 in. and the radius is half of the diameter.
half of 12 is 6, therefore the radius is 6 in. or r = 6
Assuming pi is 3.14, solve for the height of the cylinder
1470 = (3.14)(6²)(height)
1470 = 3.14 x 36 x height
1470 = 113.04 x height
height ≈ 13 in

Now that we know the height of the cylinder is about 13 in., we know the height of the cone, because the problem says that the height of the cone is half the height of the cylinder.
half of 13 is 6.5, therefore the height of the cone is 6.5
the radius of the cone is the same as that of the cylinder, 6 in.

volume of a cone = πr² × (height ÷ 3)

volume of the cone = (3.14)(6²)(6.5 ÷ 3)
volume of the cone = (3.14)(36)(2.16666)
volume of the cone = 244.92 in³

Now all that's left to find the volume of the whole cake is to add the volume of the cylinder to the volume of the cone.

1470 + 244.92 = 1714.92 in³

6 0

3 years ago

Please help me thank you.

IrinaVladis [17]

I believe the answer is 1. hope that helped

8 0

2 years ago

Read 2 more answers

Compare the perimeter and area of the original figure to the perimeter and area of the reduced figure using the scale factor. A

Serggg [28]

Answer:

- The scale factor is one-half

- The perimeter of the model is the product of the scale factor and the perimeter of the original rectangle

-The area of the reduced figure is (1/2)^2 = 1/4 times the area of the original figure

Step-by-step explanation:

The ratio of the length of the original rectangle to that of the reduced rectangle is 6 to 3, or a factor of 1/2. The ratio of the width of the original rectangle to that of the reduced rectangle is 2 to 1, or, again, a factor of 1/2. So, because this ratio of 1/2 is constant, we know the total scale factor is 1/2, making B correct.

The perimeter of a rectangle is: $P=2l+2w$ , where l is the length and w is the width. The perimeter of the reduced figure is: P = 2 * 3 + 2 * 1 = 6 + 2 = 8 units. The perimeter of the original figure is: P = 2 * 6 + 2 * 2 = 12 + 4 = 16 units.

Notice that 16 * (1/2) = 8, which means that the perimeter of the scale-factored, reduced rectangle is "the product of the scale factor (which is 1/2) and the perimeter of the original rectangle (which is 16)". So, C is correct.

The area of a rectangle is: $A=lw$ , where l is the length and w is the width. The area of the reduced figure is: A = 3 * 1 = 3 units squared. The area of the original figure is: A = 6 * 2 = 12 units squared.

Notice that 12 * (1/4) = 3, which means that E is correct, but D is wrong.

Hope this helps!

4 0

3 years ago

Read 2 more answers

Elimination<br> 4x-7y=5<br> 9x-7y=-15

Afina-wow [57]

Answer:

x = -4

Step-by-step explanation:

To make this easier to explain and easier to solve, we're going to first multiply the second equation of 9x-7y=-15 by -1 to make the y coefficient positive.

This results in -9x+7y=15.

When we line up the two equations on top of each other now, we'll see that both the first and second equations have opposite y coefficients, which is vital for elimination.

The next step is to add the second equation to the first one. Teachers may tell you to subtract, but I find it easier to add if you make the two y coefficients of negative value to each other.

4x-7y=5

+ -9x+7y=15

___________

-5x+0y=20, or just -5x=20, because you have successfully eliminated the y variable.

From there, you're going to solve like a normal equation (divide both sides by -5) toget you x=-4.

7 0

3 years ago

A storage shed is to be built in the shape of a box with a square base. It is to have a volume of 686 cubic feet. The concrete f

wolverine [178]

Answer:

(8.44 ft. × 8.44 ft × 9.63 ft.)

Step-by-step explanation:

A storage shed has the volume = 686 cubic feet.

686 = x²h ----------------(1)

Let the length of square base = x ft

and height of the shed = h ft

Area of concrete base = x² ft²

Cost to build the base = 8x² [since cost to build the square base = $8 per square feet]

Area of the sides of the shed = 4xh

Cost to build the sides = 4xh (3.50) [since cost to build the sides = $3.50 per square ft]

C = 14xh

Total cost = 8x² + 14xh

(C) = 8x² + (14x) × $(\frac{686}{x^2})$ = 8x² + $(\frac{9604}{x})$

To minimize the cost we will take the derivative of c and equate it to 0.

$\frac{dc}{dx}=16x-\frac{9604}{x^2}=0$

$16x = \frac{9604}{x^2}$

16x³ = 9604

x³ = $\frac{9604}{16}$

x³ = 600.25

x = 8.44 ft.

For x = 8.44

686 = (8.44)² h

h = $\frac{686}{(8.44)^2}$

= 9.63 ft

Therefore, for the minimum cost, dimension of the shed should be (8.44 ft. × 8.44 ft × 9.63 ft.)

6 0

2 years ago