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Answer :
To find the lateral area of George's conical hat, we can use the formula for the lateral surface area of a cone, which is given by:
[tex]\[ \text{Lateral Area} = \pi \times r \times l \][/tex]
where:
- [tex]\( r \)[/tex] is the radius of the base of the cone,
- [tex]\( l \)[/tex] is the slant height of the cone.
For this problem, we are given:
- The slant height ([tex]\( l \)[/tex]) is 14 inches.
- The radius ([tex]\( r \)[/tex]) is 4 inches.
Now, we can plug these values into the formula:
[tex]\[ \text{Lateral Area} = \pi \times 4 \times 14 \][/tex]
This simplifies to:
[tex]\[ \text{Lateral Area} = \pi \times 56 \][/tex]
Calculating this, the lateral area is approximately:
[tex]\[ \text{Lateral Area} \approx 175.93 \, \text{square inches} \][/tex]
When we round to the nearest square unit, the lateral area is approximately 176 square inches.
Therefore, the lateral area of the hat is 176 square inches.
The correct answer is:
176 in. [tex]\( ^2 \)[/tex]
[tex]\[ \text{Lateral Area} = \pi \times r \times l \][/tex]
where:
- [tex]\( r \)[/tex] is the radius of the base of the cone,
- [tex]\( l \)[/tex] is the slant height of the cone.
For this problem, we are given:
- The slant height ([tex]\( l \)[/tex]) is 14 inches.
- The radius ([tex]\( r \)[/tex]) is 4 inches.
Now, we can plug these values into the formula:
[tex]\[ \text{Lateral Area} = \pi \times 4 \times 14 \][/tex]
This simplifies to:
[tex]\[ \text{Lateral Area} = \pi \times 56 \][/tex]
Calculating this, the lateral area is approximately:
[tex]\[ \text{Lateral Area} \approx 175.93 \, \text{square inches} \][/tex]
When we round to the nearest square unit, the lateral area is approximately 176 square inches.
Therefore, the lateral area of the hat is 176 square inches.
The correct answer is:
176 in. [tex]\( ^2 \)[/tex]
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