What is the volume of this sphere?

Mathematics

1 answer:

Inga [223]3 years ago

6 0

Answer:

$V=2143.57\ mm^3$

Step-by-step explanation:

Given that,

The radius of the sphere, r = 8 mm

We need to find the volume of the sphere. The formula for the volume of a sphere is given by :

$V=\dfrac{4}{3}\pi r^3$

Put all the values,

$V=\dfrac{4}{3}\times 3.14\times 8^3\\\\=2143.57\ mm^3$

So, the volume of the sphere is equal to $2143.57\ mm^3$ .

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The raised vegetable garden in Susan's yard is in the shape of a rectangular prism with a volume of 48 cubic feet and a height o

Anna11 [10]

The correct question is
The raised vegetable garden in Susan's yard is in the shape of a rectangular prism with a volume of 48 cubic feet and a height of 3/4 foot. The base of the rectangular prism is not a square and the width is greater than 2 feet. What is the length and width of the rectangular prism?

let
x-------> the length of the base of the rectangular prism
y-------> the width of the base of the rectangular prism

we know that
volume of the prism=area of the base*height
volume=48 ft³
height of the prism=3/4 ft

area of the base=volume/height--------> 48/(3/4)---> 48*4/3----> 64 ft²

area of the base=64 ft²
area of the base=x*y
64=x*y--------> equation 1

y=x+2--------> equation 2

substitute equation 2 in equation 1
64=x*[x+2]-----> 64=x²+2x------> x²+2x-64=0

using a graph tool----> to resolve the second order equation
see the attached figure

the solution is
x=7.062 ft
y=x+2-----> y=7.062+2-----> y=9.062 ft

the answer is
the length of the base of the rectangular prism is 7.062 ft
the width of the base of the rectangular prism is 9.062 ft