Question

(a) Show that the volume of a metal sphere of radius 15 cm is 14140 cm”, correct to 4 significant

Answer 1

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;

$V = \dfrac{4}{3} \times \pi \times r^3$

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;

$V = \dfrac{4}{3} \times \pi \times 15^3 \approx = 14,137.16694$

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, '$V_t$', is given as follows;

$V_t$ = π × (25 cm)² × 60 cm ≈ 117809.72451 cm³

The volume of water, $V_{water}$, required to fill the tank with the sphere of volume 'V' placed inside is given as follows

$V_t$ = V + $V_{water}$

∴ $V_{water}$ = $V_t$ - V

From which we get;

$V_{water}$ ≈ 117809.72451 cm³ - 14,140 cm³ = 103,669.72451 cm³ ≈ 103,670 cm³

The volume of water required to fill the tank, $V_{water}$ ≈ 103,670 cm³.