Yes, because slope is the steepness of a line. if the steepness of those two lines are the same, you will have to expand the x-axis (the length of the first ramp).
This sort of question is answered easily by a graphing calculator. The square cut from each corner should be
1.962 inches on each side.
_____
After creating a fold-up flap of x inches in width, the base of the box will be
(10 - 2x) by (15 - 2x)
and the depth of the box will be the width of the fold-up flap: x.
Then the volume of the box is
v = x(10 -2x)(15 -2x) = 150x -50x^2 +4x^3
The derivative of the volume will be zero at the maximum volume.
0 = dv/dx = 150 -100x +12x^2
This has roots at
x = (100 ±√(100² - 4(12)(150)))/(2·12)
x = (100 ± √2800)/24 = (25 ± 5√7)/6
Only the smaller of these solutions gives a maximum volume.
You should cut
(5/6)(5-√7) ≈ 1.962 inches to obtain the greatest volume.
Answer:

Step-by-step explanation:

Given:
Volume of toy=231 cm³
Diameter of a hemisphere= 7 cm
cone and hemisphere have equal radius.
radius of hemisphere = radius of cone = 3.5 cm
Height of hemisphere= radius of hemisphere= 3.5 cm
Let H be the height of toy
H= height of cone+ height of hemisphere
H = h + r , ( h = height of cone)
H = h + 3.5
volume of toy = volume of cone + volume of hemisphere
Volume of toy= 1/3πr²h + 2/3πr³
Volume of toy=πr²/3(h+2r)
231 = (22/7)×(3.5)² ×(1/3)(h+2×3.5)
231×3 =( 22×3.5×3.5)/7 (h+7)
h+7 = (231×3×7)/(3.5×3.5×22)
h+7 = (3×3)/(.5×.5×2)
h+7= 900 /50= 90/5= 18
h+7= 18
h=18-7
h= 11 cm
Height of toy = h+r
Height of toy = 11+3.5= 14.5
Height of toy =14.5 cm
Hence, the height of the toy = 13.5 cm
You cannot calculate this.