Question

Two containers designed to hold water are side by side, both in the shape of a cylinder. Container A has a diameter of 6 feet and a height of 18 feet. Container B has a diameter of 8 feet and a height of 17 feet. Container A is full of water and the water is pumped into Container B until Container A is empty. To the nearest tenth, what is the percent of Container B that is empty after the pumping is complete?​

Answer 1

The percent of container B that is left after pumping the water of Container A full in it is 40 per cent .

Step by step Step-by-step explanation :

Given -

• Two containers ( Container A & Container B ) in shape of cylinders.
• Diameter of Container A = 6 feet
• Height of Container A = 18 feet
• Diameter of container B = 8 feet
• Height of Container B = 17 feet

To find -

The percent of container B that is left after pumping the water of Container A full in it.

Solution -

Firstly, we have to find how much water each container can hold i.e. volume of containers .

We know that -

`\boxed{ \mathfrak \purple{volume \: of \:cylinder = \pi {r}^(2) h} }`

where, r is the radius of the cylinder & h is the height of the cylinder.

Now,

For Container A

Given, diameter = 6 feet

.•. Radius =
`(6)/(2)`

`= 3 \: \mathfrak{feet}`

Height = 18 feet

•.• Volume of Container A =
`(22)/(7) * {3}^(2) * 18`

`= (22)/(7) * 3 * 3 * 18`

`= (3564)/(7)`

`= 509.142857 \:{ft.}^(3) \mathfrak{(approximately)}`

Rounding off to the nearest tenth . ..

`=> 510 \: \mathfrak{ {feet}^(3) }`

For Container B

Given, Diameter = 8 feet

.•. Radius =
`(8)/(2)`

`= 4 \: \mathfrak{feet}`

Height = 17 feet

•.• Volume of Container B =
`(22)/(7) * {4}^(2) * 17`

`= (22)/(7) * 4 * 4 * 17`

`= (5984)/(7)`

`= 854.857143 \: {ft.}^(3) \mathfrak{(approximately)}`

Rounding off to the nearest tenth. ..

`=> 850 \: \mathfrak{ {feet}^(3) }`

Now,

Volume container B that is left after pumping the water of Container A in it = Volume of Container B - Volume of Container A

= ( 850 - 510 ) ft^3

= 340 ft^3

Now ,

The percent of container B that is left after pumping the water of Container A in it = Volume container B that is left after pumping the water of Container A /Total volume of Container B × 100

`= (340)/(850) * 100`

`= \boxed{ 40 \: \%}`