1- A hemispherical dome holds a volume of 486pie ft^3. Find the surface area (omit the area of the circle. 2- If a regulation NBA basketball has a circumference of 29.5 inches, then find the...

1- A hemispherical dome holds a volume of 486pie ft^3. Find the surface area (omit the area of the circle.

2- If a regulation NBA basketball has a circumference of 29.5 inches, then find the following: diameter?  radius? surface area? volume?

Please make sure the answers are correct before posted. Thanks a lot.

Asked on by eyehawk

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llltkl | College Teacher | (Level 3) Valedictorian

Posted on

1. The volume of a hemisphere with radius r is given by:

`V=2/3pir^3`

Since the volume of the hemispherical dome is `486 pi ft^3`

`486 pi=2/3pir^3`

`rArr r^3=(486*3)/2`

`rArr r=((486*3)/2)^(1/3)`

`rArr r=9 ft`

Surface Area of a hemisphere omitting the area of the base or the circle = `2 pi r^2`

Substituting the value of `r` we get the surface area =

`2*pi*(9)^2`

`=162 pi ft^2`

Therefore, the surface area of the hemispherical dome is `162pi ft^2` .

2. Circumference of the basketball=29.5 inches

So, `2pir=29.5`

`rArr r=29.5/(2pi)`

Taking `pi=3.14` ;

radius=4.7 inches

Hence, diameter=2*radius=2*4.7=9.4 inches

Surface area of the basketball

`=4pir^2`

`=4*3.14*4.7^2`

=277.5 in^2

Volume of the basketball:

`=4/3pir^3`

`=4/3*3.14*(4.7)^3`

`=434.7 ` in^3

Sources:

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