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3 years ago

Find the height of a cone with a volume of 942 cubic units and a radius of 10 units

1 answer:

3 0

Volume of a cone: $\frac{1}{3}$ $\pi$ r²h
Plug the radius and volume in the formula.

$\frac{1}{3}$ $\pi$ 10²h = 942
Divide both sides by $\frac{1}{3}$ .

$\pi$ 10²h = 2,826
Divide both sides by pi.

10²h = 900
Divide both sides by 10² (100).

h = 9

The cone's height is 9 units.

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3 years ago

QUESTION 2. the feasible region shows the number of chairs x and tables y that a furniture company can build each week.

GalinKa [24]

Answer:

Part a) The company can not build 12 chairs and 5 tables

Part b) The company can build 18 chairs and 3 tables

Part c) The company can build 12,13,14,15,16 or 17 chairs

Step-by-step explanation:

we know that

If a ordered pair is a solution, then the ordered pair must be belong to the feasible region of the graph

Part a) Can the company build 12 chairs and 5 tables?

In this problem we have the ordered pair A(12,5)

Plot and verify if the point belong to the feasible region of the graph

see the attached figure to better understand the problem

The point A is not on the feasible region

therefore

The company can not build 12 chairs and 5 tables

Part b) Can the company build 18 chairs and 3 tables?

In this problem we have the ordered pair B(18,3)

Plot and verify if the point belong to the feasible region of the graph

see the attached figure to better understand the problem

The point B is on the feasible region

therefore

The company can build 18 chairs and 3 tables

Part c) One week, the company decides to build 4 tables. how many chairs can the company build?

For y=4

Find the value of x in the graph

The solutions point for y=4 tables are

(12,4), (13,4),(14,4),(15,4),(16,4) and (17,4)

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3 years ago

An open box is to contain a volume of 3 cubic meters. Given that the material forthe sides of the box costs 6 per square meter a

bekas [8.4K]

Answer: total cost = 36/w + 36/l + 9lw

Step-by-step explanation:

The formula for determining the volume of the rectangular box is expressed as

Volume = lwh

Where lwh represents the length, width and height of the box respectively.

Since the volume of the box = 3cm³,then

lwh = 3

h = 3/lw

Since the box is open, the surface area would be

2lh + 2wh + lw

Given that the material for the sides of the box costs 6 per square meter, the total cost for the sides is

(2lh × 6) + (2wh × 6)

Substituting h = 3/lw into the above expression, it becomes.

(2l × 3/lw × 6) + (2w× 3/lw × 6)

= 36/w + 36/l

Since the material for the bottom costs 9per square meter, the total cost for the bottom is

9 × lw = 9lw

Therefore, the total cost of the box as a function of the length land width is

36/w + 36/l + 9lw

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3 years ago

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2 years ago