A homeowner purchases insulation for her attic rated at R-15. She wants the attic insulated to R-30. If the insulation she purchased is 10cm thick, what thickness does she need to use ?

Options

A. 10cm
B. 15 cm
C. 20 cm
D. 30 cm

Answer

To solve the problem, we need to determine the thickness of insulation required to achieve an R-value of R-30, given that the homeowner has already purchased insulation rated at R-15 with a thickness of 10 cm.

### Step-by-Step Solution:

1. **Understand the R-value**: The R-value is a measure of thermal resistance. The higher the R-value, the better the insulation. The homeowner currently has insulation rated at R-15 and wants to achieve R-30.

2. **Determine the required increase in R-value**:
\[ \text{Required R-value} = R-30 \]
\[ \text{Current R-value} = R-15 \]
\[ \text{Increase in R-value} = R-30 - R-15 = R-15 \]

3. **Relate thickness to R-value**: The R-value is directly proportional to the thickness of the insulation. If the insulation thickness is doubled, the R-value also doubles.

4. **Calculate the thickness needed for R-30**:
- Since the homeowner's current insulation (10 cm) provides R-15, to achieve R-30, she needs to double the thickness.
\[ \text{Required thickness} = 10 \, \text{cm} \times 2 = 20 \, \text{cm} \]

5. **Conclusion**: The homeowner needs to use insulation that is 20 cm thick to achieve the desired R-30 rating.

### Final Answer:
The thickness of insulation needed to achieve R-30 is **20 cm**.

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