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BlackZzzverrR [31]
3 years ago
13

A local hockey rink is covered by a dome in the shape of a hemi-sphere (half sphere). if the floor of the arena has a diameter o

f 250 ft, what is the surface area of the domed roof to the nearest square foot?
Mathematics
1 answer:
8_murik_8 [283]3 years ago
5 0

The surface area of hemisphere is given by:

Surface Area = 2 \pi r^{2}

Where r is radius of hemisphere.

We are given diameter = 250 ft.

We know that radius = half of diameter.

Radius of dome = 1/2 (250) = 125 ft.

Now let us plug the value of radius in the formula,

Surface Area = 2 (3.14) (125)^{2}

Surface Area of dome = 98125 square foot.

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<h2>\large\bold{\underline{\underline{Question:-}}}</h2>

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\underline{ \underline{ \sf{Let's \:  find  \: the  \: ratio  \: of \:  their  \: volumes:}}}

{ \implies{ \sf  {V _{1}  :  V_{2}}}}

{ \implies{ \sf{ \frac{1}{3} \pi \:  { r_{1}}^{2}  h_{1} :  \frac{1}{3}  \pi \:  { r_{2} }^{2}  h_{2}}}}

{ \implies{ \sf{ {r_{1}}^{2}  h_{1} :  { r_{2}}^{2} h_{2}}}}

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{ \implies{ \sf{ \frac{ {3}^{2} }{ {1}^{2} }  :  \frac{3}{1} }}} \\

{ \implies{ \sf{ \frac{9}{1} :  \frac{3}{1}  }}} \\

{ \implies{ \sf{3 : 1}}} \\

{ \therefore{ \sf{ \green{Ratio  \: of  \: their \:  volumes = 3 : 1}}}}

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