For a scale of 1 cm:12 km, find the actual length represented by the length 1.7 cm in a drawing

A cylinder has a 12-inch diameter and is 15 inches tall. It is filled to the top with water. A 6-inch-diameter ball is placed wi

Tems11 [23]

The volume of the cylinder is the space occupied by the cylinder. The volume of the water in the cylinder is 1583.36266 in³.

<h3>What is the volume of a cylinder?</h3>

The volume of the cylinder is the space occupied by the cylinder. It is calculated with the help of the formula,

$\text{Volume of the cyllinder}= \pi r^2h$

As it is given that the diameter of the cylinder is 12 inches while the height of the cylinder is 15 inches, also, it has a ball of the diameter of 6 inches placed inside the cylinder, therefore, the volume of the water that is inside the cylinder is the difference in the volume of the cylinder and the volume of the spherical ball.

$\text{Volume of the cyllinder}= \pi r^2h = \dfrac{\pi}{4}d^2 h$

Substitute the values,

$\begin{aligned}\text{Volume of the cyllinder}&= \dfrac{\pi}{4}d^2 h\\& = \dfrac{\pi}{4} \times (12^2) \times 15\\ &=1696.46\rm\ in^3\end{aligned}$

Now, the volume of the ball is equal to the volume of the sphere therefore, the volume of the ball can be written as,

$\text{Volume of the sphere} = \dfrac{4}{3}\pi r^3$

$= \dfrac{4}{3}\pi r^3\\\\= \dfrac{4}{3}\times \pi \times (3^3)\\\\= 113.097\rm\ in^3$

Further, the volume of the water that is inside the cylinder can be written as,

The volume of water = Volume of the cylinder - Volume of the sphere

= 1696.46 - 113.097

= 1583.36266 in³

Hence, the volume of the water in the cylinder is 1583.36266 in³.

Learn more about Volume of the Cylinder:

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5 0

2 years ago

Kate baked a berry pie. The recipe called for 7 ounces of blackberries, 7 ounces of raspberries, and 6 ounces of strawberries. I

saul85 [17]

Answer:

Step-by-step explanation:

The recipe for baking a berry pie called for 7 ounces of blackberries, 7 ounces of raspberries, and 6 ounces of strawberries.

Since she only found 12-ounce containers of berries, she bought 1 container of each kind of berry.

After she baked the pie,

The number of ounces of blackberries left would be 12 - 7 = 5 ounces.

The number of ounces of raspberries left would be 12 - 7 = 5 ounces.

The number of ounces of strawberries left would be 12 - 6 = 6 ounces.

Total number of ounces of berries that Kate has left would be

5 + 5 + 6 = 16 berries

3 0

3 years ago

$580, 2%, 6 months Simple interest

Helen [10]

Answer:

$580 2% a month for 6 months equals $649.60

Step-by-step explanation:

$580*0.02=$11.6

$11.6*6=$69.6

$580+$69.6=

$649.6

0.02 equals 2 percent as a decimal

6 0

3 years ago

I need help with this question please

Usimov [2.4K]

Answer:

The slope will be the same for a straight line no matter which two points you pick as you know. All you need to do is to calculate the difference in the y coordinates of the 2 points and divide that by the difference of the x coordinates of the points(rise over run). That will give you the slope.

7 0

3 years ago

Read 2 more answers

Write an equation in slope intercept form (4,-2) (0,-5)

Zarrin [17]

Answer:

y=-7/4x+5

Step-by-step explanation:

The line contains points at (4,-2) and (0,-5)

(y1-y2) / (x1-x2) = slope

(4,-2) =(x1,y1)

(0,-5) = (x2,y2)

(-2-5) / (4-0)

-7 / 4 = -7/4

y= -7/4x + b

plug in points for x and y to find b

-2=-7/4(4)+b

-2=-7+b

5=b

y=-7/4x+5

7 0

3 years ago