8. The base of a circular cone has a diameter of 10 cm and an altitude of 10 cm. The cone is filled with water. A sphere is lowered into the cone until it just fits. Exactly one-half of the sphere remains out of the water. Once the sphere is removed, how much water remains in the cone?

Answers

Answer 1

Answer:

Answer:

The volume of water that remains on the cone is 523.6 cm³

Step-by-step explanation:

To solve this problem you have to keep in mind the formules that describes the volume of a cone and the volume of a sphere.

Volume of a cone = (πr²h)/3

Volume of a sphere = (4/3)πr³

So, if the base of the cone has a diameter of 10 cm, its radius is 5 cm. Its altitude is 10 cm. ⇒Volume = (πr²h)/3 ⇒ Volume = [π(5²)10) ⇒

Volume = 785.4 cm³. This is the initial volume of water.

Now if the sphere fits in the cone and half of it remains out of the water, the other half is inside the cone. Estimating the volume of the sphere and dividing it by two, you find the volume of water that was displaced.

Volume of a sphere = (4/3)πr³, here the radius is the same of the base of the cone (5 cm).

⇒ Volume = (4/3)π(5³) ⇒ Volume = 523.6 cm³ ⇒ The half of this volume is 261.8 cm³. This is the volume of water displaced.

⇒ The volume of water that remains on the cone is 523.6 cm³ (785.4 cm³- 261.8 cm³)

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Jermaine buys T-shirts for $6 each and marks up the price by 45%. How much profit does Jermaine make for each T-shirt sold?

Answers

Answer:

$2.70

Step-by-step explanation:

Cost price = $6

Mark up percentage = 45%

Mark up amount = 45% × $6

= 0.45 × $6

= $2.70

Selling price = Mark up + cost price

= $2.70 + $6

= $8.70

Jermaine sells the shirts for $8.70 and makes a profit of $2.70.

Answer:

$2.70

Step-by-step explanation:

6*45% =2.70

The diameter of the base of the cone measures 8 units.The height measures 6 units.
What is the volume of the cone?
A)240 cubic units
B)321 cubic units
C)48X cubic units
D)647 cubic units

Answers

Answer: $32\pi$ cubic units.

Step-by-step explanation:

You can use this formula for calculate the volume of a cone:

$V_(cone)=(1)/(3)\pi r^2h$

Where "r" is the radius and "h" is the height.

You know that the diameter of the base of the cone measures 8 units, then, the radius can be found by dividing the diameter by 2:

$r=(8units)/(2)\n\nr=4units$

Since you already know that height and the radius, you can substitute them into the formula. Then, the volume of this cone is:

$V_(cone)=(1)/(3)\pi (4units)^2(6units)$

$V_(cone)=32\pi \ units^3$

Answer:

b. 32

Step-by-step explanation:

e2020 says so

In what order do numbers go?

Answers

Answer:

What?

Step-by-step explanation:

Answer:

1 2 3 4 5 6 7 8 9 10

Step-by-step explanation:

yes yes yes

Solve 4x-2=2x-10 help

Answers

4x-2x=-10+2
2x=-8
x=-8/2
x=-4

4x - 2 = 2x - 10
4x - 2 - 2x = (2x - 10) - 2x
2x - 2 = -10
(2x - 2) + 2 = -10 + 2
2x = -8
2x / 2 = -8 / 2
x = -4

Steve built a square dog pen that has a perimeter of 240 inches. What is the length of one side of Steve's dog pen?

Answers

Perimeter of a square=4 x side
Data:
Perimeter=240 in

Then:
240 in=4* side
side=240 in/4
side=60 in.

answer: The lenght of one side of Steve´s dog pen is 60 in.

Matt bought 7 shirts for a total of $38. Tee shirts cost $5 and long sleeve shirts cost $6. How many of each type of shirt did he buy? HELP PLZ 100 POINTS