Cheryl biked two days in a row. On the first day, Cheryl biked 6 miles at a steady pace for 15 minutes. On the second day, she biked 12 miles in 30 minutes. Cheryl claims that she rode at the same speed on both days.

(a) 1) When V = 1000 L, the height of the liquid in the tank is approximately 62 cm

2) When V = 5,000 L, the height of the liquid in the tank is approximately 106 cm

3) When V = 10,000 L, the height of the liquid in the tank is approximately 202 cm

b) The drawing of the spherical tank showing the height of the liquid level for each volume created with Microsoft Excel is attached

Step-by-step explanation:

(a) The height of the spherical tank = 3 m

The diameter of the spherical tank, d = 3 m

The capacity of the spherical tank = 14,000 L

The volume of a sphere, V = (4/3) × π × r³ =

Where, r = d/2

∴ r = 3 m/2 = 1.5 m

V = (4/3) × π × (1.5)³ ≈ 14.1371669412 m³

Using calculus, we have;

For the two halves, we have;

1) For V = 1000 L, we have;

1000 L =

When V = 1000 L, we have;

The liquid level, y ≈ 0.62 m = 62 cm

2) When V = 5,000 L, we have;

The liquid level, y ≈ 1.06 m = 106 cm

3) When V = 10,000 L, we use the height of the unfilled volume at the top which is the volume of the sphere less the 10,000 L as follows;

For the volume of the sphere of 14,000 L, we have;

Volume at the top = 14,000 L - 10,000 L = 4,000 L = 4 m³

Therefore

The height of the liquid in the tank, y = d -

∴ y = 3 m - 0.985 m = 2.015 m

The liquid level, y ≈ 2.015 m = 201.5 cm ≈ 202 cm

b) Please find attached the drawing of the spherical tank created with Microsoft Excel