Mathematics, 02.04.2020 01:25 awsome12dusk

A rectangular prism has sides that are in the ratio of 3:5:9. If the volume of the prism is 8640 cm3, then the surface area of the prism, in square millimetres, is?

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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,

Volume, V = whl ...................................(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 = $\frac{3}{17}x$

Height, h = $\frac{5}{17} x$

Length, l = $\frac{9}{17}x$

Equation (1) becomes,

$8640=(\frac{3}{17}x)(\frac{5}{17} x)(\frac{9}{17}x)$

$= 0.027478 x^{3}$

$x^{3}= \frac{8640}{0.027478}$

$x = \sqrt[3]{314432}$

= 68

Step:2

Width, w = $\frac{3}{17}x$ $= (\frac{3}{17}) (68)$ = 12 cm

Height, h $= (\frac{5}{17} )(68) = 20 cm$

Length, l $= (\frac{9}{17})(68)=36cm$

Step:3

Formula for surface area of rectangular prim,

A= 2(wl+lh+hlw)

From the values of w, l and h,

= 2 [(12)(20)+(36)(20)+(36)(12)]

= 2 (240+720+432)

= 2(1392)

= 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.

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