Question

1. ms. lu is adding a new room to her house. the room will be a cube with volume 4,913 cubic feet. what is the length of the new room? 5. the area of a square garage is 121 square feet. will it fit a car that measures 13 feet long? explain.

Explanation:

Step1: Recall cube - volume formula

The volume formula for a cube is $V = s^{3}$, where $s$ is the side - length of the cube. Given $V = 4913$ cubic feet, we need to find $s$ such that $s=\sqrt[3]{4913}$.

Step2: Calculate the cube - root

We know that $17\times17\times17=4913$. So, $\sqrt[3]{4913}=17$ feet.

Step3: Recall square - area formula for the garage

The area formula for a square is $A = s^{2}$, where $s$ is the side - length of the square. Given $A = 121$ square feet, we find $s$ by taking the square - root of 121. Since $11\times11 = 121$, $s=\sqrt{121}=11$ feet.

Step4: Compare the side - length of the garage with the length of the car

The side - length of the square garage is 11 feet, and the car is 13 feet long. Since $11<13$, the car will not fit in the garage.

Answer:

The length of the new room is 17 feet. The car will not fit in the square garage because the side - length of the garage is 11 feet which is less than the 13 - foot length of the car.