Algebra-right question for Jai
posted by Mary .
In a right triangular prism, the legs of the base are each doubled, and the height is reduced by half. How does the new volume compare to the original volume of the same prism?
A.the new volume will be 1/2 as big as the original
B.the new volume will be two times bigger than original
C. the new volume will be 1/8 as big as original
D. the new volume will be 8 times bigger than original.
the volume of a triangular prism is given by
V = (1/2)*(B*H*L)
B = base
H = height
L = length
thus the new volume becomes,
V' = (1/2)*(2*B)(2*H)*L
V' = 2*(1/2)*(B*H*L) or
V' = 2*V
thus the new volume is twice the original.
note that first statement is tricky. i interpreted it as "the legs (base and height of triangle) of the base (meaning the base of the prism, which is a right triangle) are each doubled" thus saying that both base, B, and height, H is doubled, and not 1/2 of H. that's why in V', the H is multiplied by 2.
hope this helps~ :)