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Vedmedyk [2.9K]

4 years ago

12

The diameter of the base of the cone measure 17units the height measures 15units what is the unfilled volume inside the cylinder

1 answer:

777dan777 [17]4 years ago

4 0

Answer:

V = 1134.9

Step-by-step explanation:

Since $V=\pi r^{2}\frac{h}{3}$

Firstly we need to divide 17 by 2 to get the radius which is 8.5

Then we need to solve by putting the values in...

$=\pi$ x $8.5^{2}$ x $\frac{15}{3}$

= 1134.9

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A closed box with a square base is to have a volume of 171 comma 500 cm cubed. The material for the top and bottom of the box co

Zepler [3.9K]

Answer:

$C(x)=\dfrac{20x^3+1715000}{x}\\$Minimum cost, C(35)=\$29,400$

The dimensions that will lead to minimum cost of the box are a base length of 35 cm and a height of 140 cm.

Step-by-step explanation:

Volume of the Square-Based box=171,500 cubic cm

Let the length of a side of the base=x cm

Volume $=x^2h$

$x^2h=171,500\\h=\dfrac{171500}{x^2}$

The material for the top and bottom of the box costs $10.00 per square centimeter.

Surface Area of the Top and Bottom $=2x^2$

Therefore, Cost of the Top and Bottom $=\$10X2x^2=20x^2$

The material for the sides costs $2.50 per square centimeter.

Surface Area of the Sides=4xh

Cost of the sides=$2.50 X 4xh =10xh

$\text{Substitute h}$=\dfrac{171500}{x^2} $into 10xh\\Cost of the sides=10x(\dfrac{171500}{x^2})=\dfrac{1715000}{x}$

Therefore, total Cost of the box

$= 20x^2+\dfrac{1715000}{x}\\C(x)=\dfrac{20x^3+1715000}{x}$

To find the minimum total cost, we solve for the critical points of C(x). This is obtained by equating its derivative to zero and solving for x.

$C'(x)=\dfrac{40x^3-1715000}{x^2}\\\dfrac{40x^3-1715000}{x^2}=0\\40x^3-1715000=0\\40x^3=1715000\\x^3=1715000\div 40\\x^3=42875\\x=\sqrt[3]{42875}=35$

Recall that:

$h=\dfrac{171500}{x^2}\\Therefore:\\h=\dfrac{171500}{35^2}=140cm$

The dimensions that will lead to minimum costs are base length of 35cm and height of 140cm.

Therefore, the minimum total cost, at x=35cm

$C(35)=\dfrac{20(35)^3+1715000}{35}=\$29,400$

8 0

3 years ago

HELP RIGHT NOW PLEASE! The perimeter of the rectangle below is 94 units. Find the length of side PS. Write your answer without v

kondor19780726 [428]

Answer:

22

Step-by-step explanation:

so permeter of a square is the sum of all the sides

94=5x+5x+4x+2+4x+2

so x=5

then simply subistitue 5 in 4x+2

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3 years ago