K, Q1.A sqhere of radius 5cm is lowered into a rectangular tank 50cm long and 20cm wide containing water to a deqth of 10cm.The sqhere floats with half of its surface above the level of the surface of the water.Calculate (a)the volume of the sqhere, (b)the volume of water in the tank (cccc)the surface area of the sqhere above the water.=
volume of sphere
= (4/3)π5^3 = 500π/3 cm^3
volume of water in tank
= (50)(20)(10) cm^3
= 10,000 cm^3
surface area of half the sphere
= (1/2)(4π(5^2))
= 50π cm^2
This question does not look complete.
It has so much more potential than these 3 straightforward questions.
To solve this problem, we need to calculate the volume of the sphere, the volume of the water in the tank, and the surface area of the sphere above the water.
(a) To find the volume of the sphere, we can use the formula:
V = (4/3) * π * r^3
Given that the radius (r) of the sphere is 5 cm, we substitute the value into the formula:
V = (4/3) * π * (5 cm)^3
V = (4/3) * π * 125 cm^3
V ≈ 523.6 cm^3
Therefore, the volume of the sphere is approximately 523.6 cm^3.
(b) To find the volume of water in the tank, we can use the formula for the volume of a rectangular prism:
V = length * width * height
Given that the tank is 50 cm long, 20 cm wide, and the water depth is 10 cm, we substitute the values into the formula:
V = 50 cm * 20 cm * 10 cm
V = 10,000 cm^3
Therefore, the volume of water in the tank is 10,000 cm^3.
(c) To find the surface area of the sphere above the water, we need to calculate the surface area of the complete sphere and then subtract the surface area submerged in the water.
The formula for the surface area of a sphere is:
A = 4 * π * r^2
Given that the radius (r) of the sphere is 5 cm, we substitute the value into the formula:
A = 4 * π * (5 cm)^2
A = 4 * π * 25 cm^2
A = 314.16 cm^2
Since the sphere floats with half its surface area above the water, we only need to calculate the area of half the sphere:
Half of the sphere's surface area = 314.16 cm^2 / 2
Half of the sphere's surface area = 157.08 cm^2
Therefore, the surface area of the sphere above the water is 157.08 cm^2.