Question

Consider a tank in the shape of pyramid with height 12 m and square base of length 2 m. The base is sitting on the ground. It is partially filled with water --- the water is 6 m deep. (A). Sketch the pyramid, choose a coordinate system, and label it on the sketch. Slice the pyramid into horizontal slices each with height $Delta x$ (or $Delta y$) cm and sketch one of the slices. (B). Find the approximate volume of the slice that is a vertical distance $x_i$ (or $y_i$) cm from the tip (or base) of the pyramid. The only variables in your answer should be ($x_i$ and $Delta x$) or ($y_i$ and $Delta y$). (C). Set up, but do not evaluate, a definite integral that calculates the volume of water inside the tank. (Recall that the water is 6 m deep.)

          Consider a tank in the shape of pyramid with height 12 m and square base of length 2 m. The base is sitting on the ground. It is partially filled with water --- the water is 6 m deep.
(A). Sketch the pyramid, choose a coordinate system, and label it on the sketch. Slice the pyramid into horizontal slices each with height $Delta x$ (or $Delta y$) cm and sketch one of the slices.
(B). Find the approximate volume of the slice that is a vertical distance $x_i$ (or $y_i$) cm from the tip (or base) of the pyramid. The only variables in your answer should be ($x_i$ and $Delta x$) or ($y_i$ and $Delta y$).
(C). Set up, but do not evaluate, a definite integral that calculates the volume of water inside the tank. (Recall that the water is 6 m deep.)

Consider a tank in the shape of pyramid with height 12 m and square base of length 2 m. The base is sitting on the ground. It is partially filled with water — the water is 6 m deep.
(A). Sketch the pyramid, choose a coordinate system, and label it on the sketch. Slice the pyramid into horizontal slices each with height Delta x (or Delta y) cm and sketch one of the slices.
(B). Find the approximate volume of the slice that is a vertical distance xi (or yi) cm from the tip (or base) of the pyramid. The only variables in your answer should be (xi and Delta x) or (yi and Delta y).
(C). Set up, but do not evaluate, a definite integral that calculates the volume of water inside the tank. (Recall that the water is 6 m deep.)

Added by Fernando R.

Question

Please give Ace some feedback