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docker41 [41]
3 years ago
12

what is the exact circumference of the base of a cone that has a volume of 1014 pi in^3 and a height of 18 in.

Mathematics
1 answer:
Evgen [1.6K]3 years ago
8 0
\bf \textit{volume of a cone}\\\\
V=\cfrac{\pi r^2 h}{3}\quad 
\begin{cases}
r=radius\\
h=height\\
-----\\
V=1014\pi \\
h=18
\end{cases}\implies 1041\pi =\cfrac{\pi \cdot r^2\cdot 18}{3}
\\\\\\
1041\pi =6\pi r^2\implies \cfrac{1041\pi }{6\pi }=r^2\implies \cfrac{347}{2}=r^2\implies \boxed{\sqrt{\cfrac{347}{2}}=r}\\\\
-------------------------------\\\\
\textit{circumference of a }\stackrel{cone's}{circle}\\\\
C=2\pi r\qquad \qquad C=2\pi \left( \boxed{\sqrt{\cfrac{347}{2}}} \right)
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Clare has a recipe for yellow cake. She uses 913 cups of flour to make 4 cakes. Noah will follow the same recipe. He will make c
sergejj [24]

Answer:

(C)c= \frac{3}{7}f

Step-by-step explanation:

Clare uses 9\frac{1}{3} cups of flour to make 4 cakes.

It means  she uses 1 cup of flour to make 4\div9\frac{1}{3} cakes.

Let us simplify that expression first for future use.

4\div9\frac{1}{3}=4\div\frac{28}{3} =4 X \frac{3}{28} =\frac{3}{7}

Therefore, Clare uses 1 cup of flour to make \frac{3}{7} cakes.

If Noah follows the same recipe,

He uses f cups of flour to make c cakes

Using Ratio Method

→  Name  :  Cup  :  Cake

→  Clare   :    1        :   \frac{3}{7}

→  Noah   :     f       :   c

By using cross multiplication

c X 1 = \frac{3}{7}f

c= \frac{3}{7}f

The equation c= \frac{3}{7}f represents the relationship between c and f

8 0
3 years ago
Point A is located at (3,4) and is rotated 90 degrees counterclockwise about the origin. What is the new point of A?
sineoko [7]

A'(- 4, 3 )

Under a counterclockwise rotation about the origin of 90°

a point (x, y ) → (- y, x )

A(3, 4 ) → A'(- 4, 3 )


5 0
3 years ago
The volumes of two cubes are 32ft^3 and 1372ft^3
ser-zykov [4K]

Answer:

1) 8 : 343

2) 42.875 or 42 ⅞

3) 4 : 49

4) 16ft²

Step-by-step explanation:

Volume of cube: s³

Surface area of cube: 6s²

_____________________

32ft^3 and 1372ft^3 →

32 : 1372 = 8 : 343

343 / 8 = 42 ⅞ = 42.875

s³ → 6s²

s³ = 8, s = 2, s² = 4.

s³ = 343, s = 7, s² = 49.

These are proportional so it is already in the simplest ratio so it is not necessary to multiply by 6.

s³ → 8 : 343

6s² → 4 : 49

(4 / 49) × 196ft² = 16ft²

4 0
3 years ago
Eli has saved $48.50. Eli's brother borrowed 1/10 of Eli's savings. How much money does Eli have left?
zimovet [89]

Answer:

$43.65

Step-by-step explanation:

1. divide 48.50 by 10

4.85

2. subtract 4.85 from 48.50

3. your answer would be $43.65

5 0
2 years ago
Read 2 more answers
Solve by any method from this unit. y2 - 5y = 3 Please help
ExtremeBDS [4]

Answer:

-1

Step-by-step explanation:

First we combine like terms, so y2 - 5y = - 3y

Now we get - 3y = 3

Then we divide both sides by - 3

Now we get y =-1

7 0
2 years ago
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