All categories

3 years ago

A hollow sphere sits snugly in a foam cube so that the sphere touches each side of the cube. Find the volume of the foam.

Mathematics

1 answer:

ExtremeBDS [4]3 years ago

5 0

Answer:

V-foam = 4r³( 2 - ----- )

Step-by-step explanation:

Let the radius of the sphere be r. Then the volume of the sphere is

V = (4/3)(π)(r³).

Next, recognize that the side length of the cube is 2r, and that the volume of the cube is thus

V = (2r)³, or 8r³.

Then the volume of the foam is equal to the volume of the cube less the volume of the sphere:

V-foam = 8r³ - (4/3)(π)(r³). This could be factored into

V-foam = 4r³( 2 - ----- )

You might be interested in

I NEEEDDDD HELPPP ASAPPPP!!! it’s urgentttttt

Artist 52 [7]

Answer:

(x + 14)² + (y – 21/2)² = 1

Step-by-step explanation:

The equation of a circle can be written as seen below

(x – h)² + (y – k)² = r²

Where (h,k) is at the center and r = radius

We are given that the radius is 1

We are also given that the center is at (-14,21/2)

So we know that r = 1, h = -14, and k = 21/2

So to find the equation of the circle we simply substitute these values into the equation of a circle

Equation of a circle: (x – h)² + (y – k)² = r²

r = 1, h = -14, and k = 21/2

Substitute values

(x – (-14))² + (y – 21/2)² = 1²

1^2 = 1

The two negative signs before the 14 cancel out and it changes to + 14

The equation of a circle with a center at (-14,21/2) and a radius of 1 is (x + 14)² + (y – 21/2)² = 1

4 0

2 years ago

Find thetwo consecutive integers whose product is 24

malfutka [58]

Answer:

There is no solution to this equation that is an integer for x.

Step-by-step explanation:

x is the first integer, and x+1 the second

$x(x+1) = 24\\x^{2} + x - 24 =0\\$

$x = \frac{-1+\sqrt{1^{2}+4*24}}{2} =\frac{-1+\sqrt{97}}{2}\\x = \frac{-1-\sqrt{1^{2}+4*24}}{2} =\frac{-1-\sqrt{97}}{2}$

5 0

2 years ago

The low temperatures for 5 days was 5, -2, -11 ,0 and-3.What was the average low temperature for those days

Daniel [21]

Data:
Average (A): ?
Arithmetic mean (A.M) = 5, -2, -11, 0, -3sum of n numbers = 5

Solving:
$A = \frac{AM}{n} = \frac{5+(-2)+(-11)+0+(-3)}{5} = \frac{5-2-11-3}{5} = \frac{\diagup\!\!\!\!3-11-\diagup\!\!\!\!3}{5} = \frac{-11}{5} = - 2.2$

Answer:

<span>The average low temperature of these days is -2.2</span>

3 0

2 years ago

Help on this? thanks (:

Alex

Answer:

Step-by-step explanation:

24-6 = 18 32-6x3=18

Hope this helped!

4 0

3 years ago

Read 2 more answers

Piece made in 32min factory cut the time by 8% then cut time by 5% how long does it take to make the piece now in min

DiKsa [7]

Answer:

27.968 mins

Step-by-step explanation:

1) we need to find 8% of 32:

32*0.08=2.56

so 8% of 32 is 2.56 mins.

we need to subtract 2.56 by 32 since its says the times was cut by 8%

32-2.56=29.44

now 5% of 29.44:

29.44*0.05=1.472

1.472 mins

29.44-1.472=27.968

Hope this helps!

4 0

3 years ago