Question

1. carmen loves to look at the little sharks in the big tank at the aquarium. look at the tank below. what is the volume of the shark tank? multiplication expression: v = ________ exponential expression: v = ______ the volume of the shark tank is ________.

Explanation:

Step1: Identify the shape and formula

The shark tank is a cube (since all sides seem equal, as one side is 10 ft). The volume \( V \) of a cube is given by the product of its length, width, and height. For a cube, length \( l \), width \( w \), and height \( h \) are all equal (let's call this side length \( s \)). So the formula for the volume of a cube is \( V = l \times w \times h \) or \( V = s \times s \times s \). Here, \( s = 10 \) ft.

Step2: Multiplication expression

Substitute \( s = 10 \) into the multiplication formula. So \( V = 10 \times 10 \times 10 \).

Step3: Exponential expression

Recall that \( s \times s \times s = s^3 \). So with \( s = 10 \), the exponential expression is \( V = 10^3 \).

Step4: Calculate the volume

Calculate \( 10 \times 10 \times 10 \) (or \( 10^3 \)). \( 10 \times 10 = 100 \), then \( 100 \times 10 = 1000 \). So the volume is 1000 cubic feet.

Answer:

Multiplication expression: \( V = 10 \times 10 \times 10 \)
Exponential expression: \( V = 10^3 \)
The volume of the shark tank is \( 1000 \) cubic feet.