Rotation 90° clockwise about the origin

6. In a toy factory, 200 wooden closed cylinders of diameter 35 mm and height 7 cm have to be painted. What is the total surface

Pachacha [2.7K]

Answer:

6) About 19,244.75 square centimeters.

7) About 4895 containers.

Step-by-step explanation:

Question 6)

We need to paint 200 wooden closed cylinders of diameter 35 mm and height 7 cm. And we want to find the total surface area that needs to be painted.

First, since the diameter is 35 mm, this is equivalent to 3.5 cm.

The radius is half the diameter, so the radius of each cylinder is 1.75 cm.

Recall that the surface area of a cylinder is given by the formula:

$\displaystyle \text{SA}=2\pi r^2+ 2\pi rh$

Where <em>r</em> is the radius and <em>h</em> is the height.

Therefore, the surface area of a single cylinder will be:

$\displasytyle \text{SA}=2(3.142)(1.75)^2+2(3.142)(1.75)(7) = 96.22375\text{ cm}^2$

Then the total surface area for 200 cylinders will be:

$\displaystyle \text{SA}_{\text{total}}=200(96.22375)=19244.75\text{ cm}^2$

Question 7)

We know that the tank has a diameter of 2.4 m and a height of 6.4 m.

Since its diamter is 2.4 m, then its radius is 1.2 m.

Find the total volume of the tank. The volume for a cylinder is given by:

$\displaystyle V=\pi r^2h$

Since <em>r</em> = 1.2 and <em>h</em> = 6.4:

$\displaystyle V=(3.142)(1.2)^2(6.4)=28.956672\text{ m}^3$

Each container has a base radius of 8.2 cm and a height of 28 cm.

So, the radius of each container is 0.082 m and the height is 0.28 m.

Then the volume of each container is:

$\displaystyle V=(3.142)(0.082)^2(0.28)=0.005915506\text{ m}^3$

Then to find the number of containers that can be filled by the tank, we can divide the two values. Hence:

$\displaystyle C=\frac{28.956672}{0.005915506}=4895.045466\approx 4895$

Thus, approximately 4895 containers can be filled.

5 0

3 years ago

Read 2 more answers

Marie has 8 hours to write a 45-page chapter

Anastasy [175]

Marie will NOT complete the chapter in time

Step-by-step explanation:

If Marie writes at a constant speed of 4 pages per hour, to write a 45-page chapter she will take;

45/4 = 11.25

= 11 ¼ hours

11 ¼ hours > 8 hours

Therefore Marie will NOT complete the chapter in time

Learn More:

For more on comparisons check out;

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7 0

3 years ago

Identify a transformation of the function f(x) = x by observing the equation of the function g(x) = x − 16.

navik [9.2K]

The transformations are

(b) A vertical shift 16 units downward.
(d) A horizontal shift 16 units to the right

<h3>How to determine the transformation?</h3>

The functions are given as:

f(x) = x

g(x)= x - 16

When a function is shifted right, the transformation rule is:

(x, y) = (x - h, y)

This means that the transformation is (d) A horizontal shift 16 units to the right

Since the parent function is a base linear function.

The transformation can also be represented as:

(x, y) = (x, k - h)

This gives

g(x)= x - 16

This means that the transformation is (b) A vertical shift 16 units downward.

Hence, the transformations are (b) and (d)

Read more about transformation at:

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8 0

1 year ago

The equation y = 5x represents a proportional relationship. what is the constant of proportionality

balandron [24]

Answer:

the constant of proportionality is 5-D

6 0

3 years ago

Gage is building a model rocket for a science fair project. He attaches a nosecone to a cylindrical body to form the rocket's fu

denpristay [2]

Answer:

305.78 in2

Step-by-step explanation:

The rocket has two parts: one is a cylinder and the other is a cone.

To find the total volume of the rocket, we need to find firstly the volume of each part.

The cylinder has a radius of 2 inches and a height of 2*12 + 5 - 7 = 22 inches, so its volume is:

V1 = pi * r^2 * h = pi * 2^2 * 22 = 276.46 in2

The cone has a radius of 2 inches and a height of 7 inches, so its volume is:

V2 = (1/3) * pi * r^2 * h = (1/3) * pi * 2^2 * 7 = 29.32 in2

Then, we have that the volume of the rocket is:

V = V1 + V2 = 276.46 + 29.32 = 305.78 in2

3 0

3 years ago