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Yuki888 [10]
2 years ago
9

The hollow sphere, in which the circus motorcyclist performs his stunts, has a diameter of 7 m. Find the area available to the m

otorcyclist for riding.
​
Mathematics
2 answers:
alexgriva [62]2 years ago
7 0

Diameter of the sphere = 7m

{Radius =\frac{7}{2} = 3.5 m}

Area available to motorcyclist for riding = Area of sphere

{= 4πr^2} \\  \\ {= 4*\frac{22}{7}*3.5*3.5} \\  \\ {= 154}.

The area available to the motorcyclist for riding is 154 m²

Anna11 [10]2 years ago
4 0

\huge\color{red} {\boxed{\tt{A}}} \color{blue} {\boxed{\tt{N}}} \color{hotpink}{\boxed{\tt{S}}} \color{blueviolet}{\boxed{\tt{W}}} \color{fuchsia}{\boxed{\tt{E}}}\color{lavender}{\boxed{\tt{R}}}

\red{ \star} \pmb{Diameter \:  of \:  the  \: sphere = 7 m}

\red{ \star} \pmb{Radius =\frac{7}{2} = 3.5 m}

\pink{\underline{ \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:   \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \: \: }}

\sf{Area  \: available \:  to \:  motorcyclist  \: for  \: riding = Area \:  of  \: sphere}

\:  \:  \:  \:  \:  \:  \:  \:  \: \: \:  \:  \:  \:  \sf{= 4πr^2}

\:  \:  \:  \:  \:  \:  \:  \:  \: \: \:  \:  \:  \: \sf{= 4*\frac{22}{7}*3.5*3.5}

\:  \:  \:  \:  \:  \:  \:  \:  \: \: \:  \:  \:  \: \sf{= 154}

<u>The area available to the motorcyclist for riding is 154 m²</u>

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Answer:

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You need to construct an open-top rectangular box with a square base that must hold a volume of exactly 475 cm3. The material fo
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Answer:

The dimensions of the box are:

x =  8,93 cm       and     h  =   5,95 cm

C(min) =  850,69 cents

Step-by-step explanation:

The volume of the box is:

V = x²*h          where    x is the side of the square base  and h the height

then    h  =  V/ x²  ⇒    h = 475 / x²

The total cost of box C is:

C  = C₁  +  4*C₂      Where C₁  and C₂  are the costs of the base and one lateral side respectevily

Then cost C =  8*x²   + 4* 6*h*x

The cost C as a function of x is

C(x)  =  8*x²  + (24* 475 /x² )*x

C(x)  =  8*x²  +  11400/x

Tacking derivatives on both sides of the equation

C´(x)  =  16*x -  11400/x²

C´(x)  =  0     ⇒    16*x  -  11400/x²  = 0

16*x³  =  11400     ⇒   x³  =  11400/16

x³ =  712,5

x  =  8,93  cm

and    h   =  475 / (8,93)²      ⇒      h  =  5,95  cm

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To check if value x = 8,93 would make C(x) minimum we go to the second derivatives

C´´(x) =  16  +  22800/x³ > 0

Then we have a minimum of C at  x = 8,93

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