Question

I apologize for the cut out on this picture. Here's the question: A company designs a container in the shape of a rectangular prism for a fruit drink. The container has a base area of A, a height of h, and a volume of V. If the company decides to increase the height by 10% and reduce the area of the base by 10%, what will be the new volume of the container in terms of V.

A. 0.99V B. 1V C. 1.05V or D. 2V

Answer 1

Step-by-step explanation:

Initial volume is given by,

V = A× h

When the height is increased by 10%, new height i.e h'

$h' = \frac{10}{100} h + h$

$h' = \frac{1}{10}h + h$

$h' = \frac{(1 + 10)}{10} h$

$h' = \frac{11}{10} h$

Similarly ,when the area of the base reduced by 10%, new area i.e A'

$A' = A - \frac{1}{10} A$

$A' = \frac{9}{10} A$

Therefore, new volume V'

V'= A'h'

$V' = \frac{9}{10} A \times \frac{11}{10} h$

$V'= \frac{99}{100} Ah$

$V'= 0.99 V$

optionA