What is the surface area of the cone to the nearest tenth? The figure is not drawn to scale.
Image: www(dot)connexus(dot)com/content/media/941080-7222013-22543-PM-660972754(dot)gif
a. 906.4 cm²
b. 571.8 cm²
c. 542.4 cm²
d. 417.8 cm²
The surface area of a cone is given by the formula A = πr² + πrℓ, where r is the radius and ℓ is the slant height.
In this case, the radius is 6 cm and the slant height is 10 cm (use the Pythagorean theorem to find ℓ: ℓ² = 8² + 6² = 100, so ℓ = √100 = 10).
Therefore, A = π(6)² + π(6)(10) ≈ 571.8 cm².
The answer is b. 571.8 cm².
To find the surface area of a cone, we need to find the area of the base and the lateral area.
1. Find the area of the base (which is a circle):
- The formula for the area of a circle is A = πr², where A is the area and r is the radius.
- Looking at the image, we can see that the radius of the circle is 6 cm.
- Substitute the value of the radius into the formula: A = π(6 cm)²
- Calculate: A = 36π cm²
2. Find the lateral area of the cone:
- The formula for the lateral area of a cone is A = πrl, where A is the lateral area, r is the radius of the base, and l is the slant height.
- Looking at the image, we can see that the slant height is 10 cm.
- Substitute the values into the formula: A = π(6 cm)(10 cm)
- Calculate: A = 60π cm²
3. Add the area of the base and the lateral area to find the total surface area:
- Total Surface Area = Base Area + Lateral Area
- Total Surface Area = 36π cm² + 60π cm²
- Total Surface Area = 96π cm²
4. To find the surface area to the nearest tenth, substitute the value of π with 3.14 and calculate:
- Total Surface Area ≈ 96(3.14) cm²
- Total Surface Area ≈ 301.44 cm²
Therefore, the surface area of the cone to the nearest tenth is 301.4 cm². None of the given options match this answer.