not drawn to scale, shows a prism of length 30cm. the cross section wyxz is a square with area 144cm^2
(i) the volume in cm^3. of the prism
144 * 30 = ?
Show working out of the question please
As it relate to first question what is the total surface area in cm2 of the prism
To find the volume of the prism, we need to multiply the area of the base (cross section) by the length.
In this case, the cross section is a square with an area of 144 cm^2. Since the cross section is not drawn to scale, we cannot determine the exact dimensions of the square. However, we can assume that the length of each side of the square is "x" cm.
Therefore, the area of the square can be expressed as x^2 = 144 cm^2.
To find the value of "x," we need to take the square root of both sides of the equation: √(x^2) = √(144 cm^2).
This simplifies to x = √144 cm.
Since the length of the prism is given as 30 cm, we can now calculate the volume by multiplying the area of the base (x^2) by the length (30 cm):
Volume = x^2 * length
Volume = (x * x) * 30 cm^3
Volume = (√144 cm * √144 cm) * 30 cm^3
Volume = (12 cm * 12 cm) * 30 cm^3
Volume = 144 cm^2 * 30 cm^3
Volume = 4320 cm^3
Therefore, the volume of the prism is 4320 cm^3.