A closed box with square base has surface area 96. Maximum volume?

64 S = 2s^2 + 4 s h = 96 \Rightarrow h = (96 - 2s^2)/(4s) = (48 - s^2)/(2s). V = s^2 h = s(48 - s^2)/2. V' = (48 - 3s^2)/2 = 0 \Rightarrow s^2 = 16, s = 4. Then h = 32/8 = 4 and V = 64.

school

Acemy

Optimization

AP Calculus AB· difficulty 3/5

96

A
$64$
check_circle
B
$32$
C
$48$
D
$96$

Explanation

S = 2s^2 + 4 s h = 96 \Rightarrow h = (96 - 2s^2)/(4s) = (48 - s^2)/(2s)

Want 10 more like this — adaptive to your weak spots?

Practice 10 like thisarrow_forward Predict my AP score

Related questions