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Answer :
- Convert $48'$ to degrees by dividing by 60: $48' = \frac{48}{60}^{\circ} = 0.8^{\circ}$.
- Add the result to $36^{\circ}$: $36^{\circ} + 0.8^{\circ} = 36.8^{\circ}$.
- Calculate the side length of the cube by taking the cube root of the volume: $s = \sqrt[3]{27} = 3$.
- State the final answers: $36.8^{\circ}$ and $3$ cm. $\boxed{36.8^{\circ}}$ $\boxed{3 cm}$
### Explanation
1. Converting minutes to degrees
Let's tackle this problem step by step! First, we need to convert $36^{\circ} 48'$ into degrees. We know that there are 60 minutes in a degree, so we can convert 48 minutes into degrees by dividing 48 by 60.
2. Adding degrees
We have $48' = \frac{48}{60}^{\circ} = 0.8^{\circ}$. Therefore, $36^{\circ} 48' = 36^{\circ} + 0.8^{\circ} = 36.8^{\circ}$.
3. Finding the side length of the cube
Now, let's find the length of the cube. We are given that the volume of the cube is $27 cm^3$. The volume of a cube is given by the formula $V = s^3$, where $s$ is the side length of the cube. We need to find $s$ such that $s^3 = 27$.
4. Calculating the cube root
To find the side length $s$, we take the cube root of the volume: $s = \sqrt[3]{27} = 3$. Therefore, the length of the cube is 3 cm.
### Examples
Understanding angles and volumes is crucial in many real-world applications. For example, architects use angles to design buildings and volumes to calculate the amount of material needed. Similarly, in medicine, angles are used in radiology, and volumes are important for calculating dosages.
- Add the result to $36^{\circ}$: $36^{\circ} + 0.8^{\circ} = 36.8^{\circ}$.
- Calculate the side length of the cube by taking the cube root of the volume: $s = \sqrt[3]{27} = 3$.
- State the final answers: $36.8^{\circ}$ and $3$ cm. $\boxed{36.8^{\circ}}$ $\boxed{3 cm}$
### Explanation
1. Converting minutes to degrees
Let's tackle this problem step by step! First, we need to convert $36^{\circ} 48'$ into degrees. We know that there are 60 minutes in a degree, so we can convert 48 minutes into degrees by dividing 48 by 60.
2. Adding degrees
We have $48' = \frac{48}{60}^{\circ} = 0.8^{\circ}$. Therefore, $36^{\circ} 48' = 36^{\circ} + 0.8^{\circ} = 36.8^{\circ}$.
3. Finding the side length of the cube
Now, let's find the length of the cube. We are given that the volume of the cube is $27 cm^3$. The volume of a cube is given by the formula $V = s^3$, where $s$ is the side length of the cube. We need to find $s$ such that $s^3 = 27$.
4. Calculating the cube root
To find the side length $s$, we take the cube root of the volume: $s = \sqrt[3]{27} = 3$. Therefore, the length of the cube is 3 cm.
### Examples
Understanding angles and volumes is crucial in many real-world applications. For example, architects use angles to design buildings and volumes to calculate the amount of material needed. Similarly, in medicine, angles are used in radiology, and volumes are important for calculating dosages.
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