a sqyuare based pyramid is on top of a cube .both shapes have the same base and the same height. which expression repreents the total volume of this shape? justify your answer
What are your choices?
What did you not like about my answer yesterday?
http://www.jiskha.com/display.cgi?id=1273956086
thanks.
my choices are:
A. v=4b^4h^2 divided by 3
B. v=2b^4h^2 divided by 6
C. v=4b^2h divided by3
D. v=2b^2h divided by 3
E. v=4b^4h^2 divided by 6.
this is for ms.sue.
Ted, neither in todays nor in yesterdays post did you give any dimensions.
Your choices of answers suggest that the base had side b and the height was h
so matching my answer of (4/3)x base area x height
would be C. 4b^2h/3 or (4/3) b^2 h
To calculate the total volume of the shape, we need to find the individual volumes of the pyramid and the cube and add them together.
The volume of a square-based pyramid can be found using the formula:
Volume = (1/3) * base area * height
The base area of a square-based pyramid is equal to the area of the square base, which is side length squared.
So, let's assume that the side length of the base and the height of both the pyramid and the cube are represented by "s".
The volume of the pyramid can be calculated as:
Volume of pyramid = (1/3) * s^2 * s or (1/3) * s^3
The volume of a cube can be found by cubing the side length:
Volume of cube = s^3
Since both the pyramid and the cube have the same base and height, their volumes are equal, so we can represent the total volume of the shape as the sum of the volumes of both shapes:
Total volume = Volume of pyramid + Volume of cube
= (1/3) * s^3 + s^3
To justify this expression, we recognize that both the pyramid and the cube share the same base and height, so their volumes are additive in this configuration. By applying the respective formulas for the volume of a pyramid and a cube, we arrive at the expression (1/3) * s^3 + s^3 to represent the total volume of the shape.