Respuesta :
Answer:
a) The volume of the sphere is approximately 14,137.16694 which is 14,140 cm³ correct to 4 significant figures
b) The volume of water required to fill the tank is approximately 103,670 cm³
Step-by-step explanation:
a) In the question, the radius of the sphere, r = 15 cm
The formula for the volume, 'V', of a sphere is given as follows;
[tex]V = \dfrac{4}{3} \times \pi \times r^3[/tex]
Where;
r = The radius of the the sphere
V = The volume of the sphere
Plugging in the value for the radius, 'r', of the sphere, in the equation for, 'V', we get;
[tex]V = \dfrac{4}{3} \times \pi \times 15^3 \approx = 14,137.16694[/tex]
Therefore;
The volume of the sphere to 4 significant figures is V ≈ 14,140 cm³
b) The parameters of the cylindrical tank are;
The height of the cylindrical tank, h = 60 cm
The radius of the cylindrical tank, r = 25 cm
The volume of a cylinder, V = π·r²·h
∴ The volume of the cylindrical tank without water, '[tex]V_t[/tex]', is given as follows;
[tex]V_t[/tex] = π × (25 cm)² × 60 cm ≈ 117809.72451 cm³
The volume of water, [tex]V_{water}[/tex], required to fill the tank with the sphere of volume 'V' placed inside is given as follows
[tex]V_t[/tex] = V + [tex]V_{water}[/tex]
∴ [tex]V_{water}[/tex] = [tex]V_t[/tex] - V
From which we get;
[tex]V_{water}[/tex] ≈ 117809.72451 cm³ - 14,140 cm³ = 103,669.72451 cm³ ≈ 103,670 cm³
The volume of water required to fill the tank, [tex]V_{water}[/tex] ≈ 103,670 cm³.
