Question

A cylindrical tank of water with radius 10.5cm and height 20cm is emptied into another cylindrical tank of radius 10cm. Find the height of the new tank to 2 decimal places. Take π(22/7)

Answer 1

The height of the new cylindrical tank is approximately 54.10 cm when rounded to two decimal places.

Step-by-step explanation:

Find the volume of the water in the original tank using the formula for the volume of a cylinder:

V1 = π(10.5cm)^2(20cm) ≈ 6939.25 cm^3

Since the amount of water is conserved, set the volume of the water in the new tank equal to V1:

V2 = π(10cm)^2(h)

π(10.5cm)^2(20cm) = π(10cm)^2(h)

Simplifying, we get:

4410 = 100h

h ≈ 44.10 cm

However, this is the height that the water would reach if it was poured into a cylinder with a radius of 10 cm. To find the actual height of the new tank, add the radius of the new tank (which is also 10 cm) to this height:

h_new = h + r = 44.10 + 10 = 54.10 cm

Therefore, the height of the new tank is approximately 54.10 cm when rounded to two decimal places.

Answer 2

To find the height of the new tank, we can use the fact that the volume of a cylinder is equal to the product of its base area and its height. We calculate the volume of the first tank and then use that to find the height of the new tank.

Step-by-step explanation:

To find the height of the new tank, we can use the fact that the volume of a cylinder is equal to the product of its base area and its height. The volume of the first tank, which is being emptied, can be calculated as V = πr2h, where r is the radius and h is the height. Substituting the given values, we get V = 3.142 x (10.5 cm)2 x 20 cm. Once we have the volume of the water, we can use the formula V = πr2h again to find the height of the new tank, with the volume equal to the amount of water transferred. The radius of the new tank is given as 10 cm, so we would have V = 3.142 x (10 cm) x h. Now we can solve this equation for h to find the height of the new tank.

Calculations:

Volume of the first tank = 3.142 x (10.5 cm)2 x 20 cm = 9.278 cm³

Volume of wared to the new tank = 9.278 cm³

Volume of the new tank = 3.142 x (10 cm)2 x h, where h is the height of the new tank

Solving for h, we have 3.142 x (10 cm)2 x h = 9.278 cm³

h = 9.278 cm³ / (3.142 x (10 cm)2)

Answer:

The height of the new tank is approximately 2.96 cm.