A right rectangular prism is packed with cubes of side length Fraction 1 over 2 inch. If the prism is packed with 5 cubes along the length, 3 cubes along the width, and 6 cubes along the height, what is the volume of the prism?
Answers
Since each cube edge is = 1/3 inch,
the volume is simply
(6/3) x (4/3) x (8/3) in³
which can be rewritten as
V = 2 x [(4 x 8)/(3 x 3)] in³ = [2 x (32/9)] in³ = 64/9 in³
Hopes it helps
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Concept:
The total number of cubic units that a cube occupies in three dimensions is its volume. Six faces, twelve edges, and eight vertices make up the three-dimensional shape of a cube. Therefore, the area encircled by a cube's six faces is considered to equal its volume. It differs from 2D shapes in that it adds a third dimension, known as height or thickness, in addition to length and breadth. Since the product of a cube's length, width, and height determines its volume. Cubic units are used to measure it. The volume of a cube increases as the value of its dimensions increases.
Volume of the cube= a³
where, a= side length
Given:
A right rectangular prism is packed with cubes of side length Fraction 1 over 2 inch. If the prism is packed with 5 cubes along the length, 3 cubes along the width, and 6 cubes along the height
Find:
WHAT IS THE VOLUME OF THE PRISM
Solution:
Volume of each cube= (1/2)³
=1/8
Total no. of cubes = 5 x 3 x 6
=90
Total volume of cubical prism = 90 x 1/8
=11.25 in³
Therefore, the volume of cubical prism =11.25 in³
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