Question

a water tank with a radius of 4 meters and a height of 8 meters is full of water. another water tank has a radius of 8 meters and a height of 8 meters, but is empty. click on sections of the tank to fill it with the same amount of water as the full water tank. top view r = 8 m top view r = 4 m h = 8 m 8 m 7 m 6 m 5 m 4 m 3 m 2 m 1 m 0 m front view front view

Explanation:

Step1: Calculate volume of first tank

The volume \( V \) of a cylinder is given by the formula \( V = \pi r^2 h \). For the first tank, \( r = 4 \) m and \( h = 8 \) m. So, \( V_1=\pi\times4^2\times8=\pi\times16\times8 = 128\pi \) cubic meters.

Step2: Let height of water in second tank be \( h_2 \)

For the second tank, \( r = 8 \) m and we need to find \( h_2 \) such that \( V_2=\pi\times8^2\times h_2=64\pi h_2 \). We want \( V_2 = V_1 = 128\pi \).

Step3: Solve for \( h_2 \)

Set \( 64\pi h_2=128\pi \). Divide both sides by \( 64\pi \): \( h_2=\frac{128\pi}{64\pi}=2 \) meters. So we need to fill the second tank up to a height of 2 meters (or the section corresponding to height 2 m, or the area/volume equivalent to height 2 m in the larger tank. Since the base area of the second tank is \( \pi\times8^2 = 64\pi \) and the base area of the first is \( 16\pi \), the ratio of base areas is \( \frac{64\pi}{16\pi}=4 \), so the height in the second tank should be \( \frac{8}{4}=2 \) m (since volume is base area times height, and volume is same, height is inversely proportional to base area). So we click the section up to height 2 m (or the area that represents a height of 2 m in the second tank, which is a quarter of the volume? Wait, no, from the front view, the height markings are 0 - 8 m. So we need to fill the second tank such that the volume of water is \( 128\pi \). As calculated, height is 2 m, so we click the part of the tank (front view) up to 2 m, or the top view area corresponding to a cylinder of height 2 m (since it's a cylinder, the top view is a circle, and the volume is related to the height. So in the front view, the height of water should be 2 m, so we click the sections from 0 m to 2 m (the bottom 2 meters of the front view, or the corresponding area in the top view that would have height 2 m).

Answer:

We need to fill the second water tank (with radius 8 m) such that the height of water is 2 meters. So in the front view, we click the sections from 0 m to 2 m (or the area corresponding to a height of 2 m in the cylindrical tank). Mathematically, the height of water in the second tank is 2 meters.