Three faces of a right rectangular prism have areas of 48, 49, and 50 cm squared. What is the volume of the prism? Express your answer to the nearest whole number.
2007-05-06 04:54:21 · 2 answers · asked by Anonymous in Science & Mathematics ➔ Mathematics
Let the rectangular prism have sides of x,y and z
Area of faces = xy, yz, xz
Volume of prism = xyz
Product of areas of the faces = xy.yz.xz
=x^2.y^2.z^2
=(xyz)^2
=Volume^2
Therefore volume = sqrt(product of areas of the faces)
=sqrt(48 * 49 * 50)
=sqrt(117600)
=342.9cm^3
=343cm^3 approx
2007-05-10 03:05:38 · answer #1 · answered by gudspeling 7 · 0⤊ 0⤋
As a rectangular prism has 6 faces and only three different
type
If you call x,y and z the base and height length
xy=48
y*z=49
z*x=60
z=60/x
y=49/z
so y= 49/60 *x and xy =49/60*x^2=48 so
x= sqrt(48*60/49)=7,6665 cm
and
V=x*y*z=7.6665*49=38cm^3(rounded to the nearest whole number)
2007-05-06 07:59:02 · answer #2 · answered by santmann2002 7 · 0⤊ 2⤋