Answer to Question #144910 in Geometry for ihatemath

Question

An inverted regular square pyramid has an altitude of 12m and with top
edge of 3m is fully–filled with water.

4. What is the volume of the water in m3?
A portion of water is to be removed so that water will be 7m deep.
5. What is the area at the surface of the water when it is 7m deep?

Answer 1

4. Given $a=3\ m, H=12\ m$

$$V=\dfrac{1}{3}a^2H$$ $$V=\dfrac{1}{3}(3\ m)^2(12\ m)=36\ m^3$$

The volume of the water is 36 m³.

5.

$$\dfrac{a}{H}=\dfrac{a_1}{H_1}=const$$

Then

$$a_1=a\cdot\dfrac{H_1}{H}$$

$$a_1=3\ m\cdot\dfrac{7\ m}{12\ m}=1.75 \ m$$

$$S_1=(a_1)^2=(1.75\ m)^2=3.0625\ m^2$$

The area at the surface of the water when it is 7m deep is 3.0625 m^2.