The volume of a sphere is `2.42cm^(3)`. The volume of 12 such spheres taking into account the significant figures is

Options

A. `29.04cm^(3)`
B. `29 cm^(3)`
C. `29.0cm^(3)`
D. `29.1cm^(3)`

Answer

To find the volume of 12 spheres given that the volume of one sphere is 2.42 cm³, we will follow these steps:

### Step 1: Calculate the total volume of 12 spheres
We start by multiplying the volume of one sphere by the number of spheres.

\[ \text{Volume of 12 spheres} = \text{Volume of one sphere} \times 12 \]
\[ \text{Volume of 12 spheres} = 2.42 \, \text{cm}^3 \times 12 \]

### Step 2: Perform the multiplication
Now we perform the multiplication:

\[ 2.42 \times 12 = 29.04 \, \text{cm}^3 \]

### Step 3: Consider significant figures
Next, we need to consider the significant figures in our result. The volume of one sphere (2.42 cm³) has three significant figures. Therefore, our final answer must also be reported with three significant figures.

### Step 4: Rounding to three significant figures
The calculated volume is 29.04 cm³. To round this to three significant figures, we look at the fourth digit (which is 0 in this case). Since it is less than 5, we do not round up.

Thus, we keep the volume as:

\[ 29.0 \, \text{cm}^3 \]

### Final Answer
The volume of 12 spheres, taking into account significant figures, is:

\[ \boxed{29.0 \, \text{cm}^3} \]

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