Respuesta :
The surface area of the rectangular prism is 278400 square millimeters, if a rectangular prism has sides that are in the ratio of 3:5:9 and the volume of the prism is 8640 cubic centimeters.
Step-by-step explanation:
The given is,
Volume of Rectangular prism - 8640 Cubic centimeters
Ratio of rectangular prism sides are 3:5:9
Step:1
Formula for volume of rectangular prism,
[tex]Volume, V = whl[/tex]...................................(1)
Where, w - width of the prism
h - Height of the prism
l - Length of the prism
Let, x - side of the rectangular prism
From given values,
Volume, V = 8640 cubic centimeters
Width, w = [tex]\frac{3}{17}x[/tex]
Height, h = [tex]\frac{5}{17} x[/tex]
Length, l = [tex]\frac{9}{17}x[/tex]
Equation (1) becomes,
[tex]8640=(\frac{3}{17}x)(\frac{5}{17} x)(\frac{9}{17}x)[/tex]
[tex]= 0.027478 x^{3}[/tex]
[tex]x^{3}= \frac{8640}{0.027478}[/tex]
[tex]x = \sqrt[3]{314432}[/tex]
[tex]= 68[/tex]
Step:2
Width, w = [tex]\frac{3}{17}x[/tex] [tex]= (\frac{3}{17}) (68)[/tex] [tex]= 12 cm[/tex]
Height, h [tex]= (\frac{5}{17} )(68) = 20 cm[/tex]
Length, l [tex]= (\frac{9}{17})(68)=36cm[/tex]
Step:3
Formula for surface area of rectangular prim,
[tex]A= 2(wl+lh+hlw)[/tex]
From the values of w, l and h,
[tex]= 2 [(12)(20)+(36)(20)+(36)(12)][/tex]
[tex]= 2 (240+720+432)[/tex]
[tex]= 2(1392)[/tex]
= 2784 Square centimeters
= 2784 × 100 square millimeters
( 1 square centimeters = 100 square millimeters )
A = 278400 square millimeters
Result:
The surface area of the rectangular prism is 278400 square millimeters, if a rectangular prism has sides that are in the ratio of 3:5:9 and the volume of the prism is 8640 cubic centimeters.
