Question

The Goodsmell perfume producing company has a new line of perfume and is

Answer 1

Given:

It is given that surface area must be less than 150 cm².

Solution:

The Maximum Volume With Total Surface Area Less  than 150 cm² is shown in the table.

From the table, it can be concluded that for r=3.00 cm and h=4.95 cm the surface area will be less than 150 cm²  and the volume will be the maximum.

$S=2\pi rh+2\pi r^2\\S=2\pi (3)(7.95)+2\pi3^2\\S=93.3+56.5\\S=149.8 \text{ cm}^2$

Calculate the volume.

$V=\pi r^2h\\V=\pi(3)^2(4.95)\\V=139.96$

Hence, the required dimensions are r=3.00 cm and h=4.95 cm.