Can you please help me with this one

Three balls are packaged in a cylindrical container as shown below. The balls just touch the top, bottom, and the sides of the c

lord [1]

Answer:

a. 5177 cm³

b. 3,451 cm³

c. 67%

Step-by-step explanation:

Given:

Diameter of each ball (d) = 13 cm

Radius of the ball (r) = radius of the cylinder = ½(13) = 6.5 cm

Height of the cylinder (h) = the sum of the diameters of the 3 balls = 3(13) = 39 cm

a. Volume of cylinder = πr²h

Plug in the values

Volume of cylinder = π*6.5²*39 = 5176.56 ≈ 5177 cm³

b. Total volume of the three balls = 3(volume of 1 ball) = 3(volume of sphere) = 3(⁴/3πr³)

Plug in the value

Total volume of the 3 balls = 3(⁴/3*π*6.5³) = 3(1150.35) = 3,451.05 ≈ 3,451 cm³

c. % of volume of the container occupied by the 3 balls = total volume of the three balls / volume of cylinder × 100

Plug in the values

= 3,451/5177 × 100

= 66.6602279

≈ 67%

6 0

3 years ago

The difference between two numbers is 16. Three times the larger number is seven times the smaller. What are the numbers?

slavikrds [6]

Answer:

12 and 28

Step-by-step explanation:

Represent the numbers using x and y. Then y - x = 16. (y is the larger one.)

Then 3y = 7x, and y = (7/3)x.

Substituting (7/3)x for y in y - x = 16, we get:

(7/3)x - x = 16.

Eliminate the fraction by multiplying all three terms by 3:

7x - 3x = 48, or 4x = 48, yielding x = 12. Then y = (7/3)(12) = 28.

5 0

3 years ago

Conveyor belts called grain elevators are used to move grain into a silo. Answer the following questions knowing that the lower

Natalka [10]

From the given information,

a. The length of the belt is 180.28 ft

b. The height of the window from the ground is 100 ft

c. The length of the ramp needed is 141.42 ft

<h3>What is the Pythagorean theorem's formula?</h3>

The Pythagorean theorem states that in a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two legs of the triangle. I.e., (hypotenuse)² = (opposite)² + (adjacent)²

<h3>Calculation:</h3>

It is given that,

The height of the silo is 150 feet

The distance from the belt to the silo is 100 feet

With the given measurements, a right-angled triangle is formed.

a. Finding the length of the belt:

From the diagram,

The height of the silo, sh = 150 ft

The base distance, sb = 100 ft

So, the length of the conveyor belt is the hypotenuse (bh) of the triangle formed.

On applying the Pythagorean theorem,

bh² = sb² + sh²

⇒ bh² = (100)² + (150)²

⇒ bh² = 32500

⇒ bh = √32500 = 50√13

∴ bh = 180.28 ft

Thus, the length of the belt is 180.28 ft.

b. Finding the height of the window from the ground:

It is given that the angle of elevation from the lower end of the belt(b) to a window(w) on the side of the silo is 45°.

This creates a special right-angled triangle. I.e.,

The angles of the new triangle are 90°- 45°. So, the third angle also becomes 45° (Since the sum of angles in a triangle is 180°)

So, the new triangle has angles of 90°- 45°- 45°

Thus, the new triangle is said to be an isosceles right angled triangle.

So, the two legs of the triangle are equal. I.e., sb = sw = 100 ft

Therefore, the height of the window from the ground(sw) is 100 ft

c. Finding the length of the ramp(bw) to the window:

Since we have

sw = 100 ft and sb = 100 ft

On applying Pythagora's theorem,

bw² = sb² + sw²

⇒ bw² = (100)² + (100)²

⇒ bw = √20000 = 141.42 ft

Therefore, the length of the ramp to the window is 141.42 ft.

Learn more about the Pythagorean theorem here:

brainly.com/question/343682

#SPJ1

3 0

2 years ago

Alan multiplies a 4-digit number by 36. How can you tell the

mafiozo [28]

The number of partial products Alan will have when he multiplies a 4-digit number by 36 is; 8 partial products.

First, we must establish that a 4-digit number will have 4 place values namely;

Thousands
Hundreds
Tens
Ones.

And since, 36 has 2 place values;

We can conclude that the number of partial products that Alan wil have is; 2× 4 = 8.