The lateral area of a cone is 555 cm^2 the radius is 15.1 cm what is the slant height to the nearest tenth of a centimeter
A. 36.8cm
B. 11.7cm
C. 83.8cm
D. 25.5cm
The lateral area of a cone is given by L = πrℓ, where r is the radius of the base and ℓ is the slant height. Here, we know L = 555 cm^2 and r = 15.1 cm. Plugging in these values, we get:
555 = π(15.1)ℓ
Solving for â„“, we have:
â„“ = 555/(Ï€(15.1))
ℓ ≈ 11.7 cm
Therefore, the slant height to the nearest tenth of a centimeter is 11.7 cm, which is option B.
To find the slant height of a cone, you can use the formula:
Slant height = √(radius^2 + height^2)
In this case, we need to find the height first. The lateral area of a cone is given by the formula:
Lateral area = π * radius * slant height
Given that the lateral area is 555 cm^2 and the radius is 15.1 cm, we can rearrange the formula:
555 = π * 15.1 * slant height
Now, let's solve for the slant height:
slant height = 555 / (Ï€ * 15.1)
Using a calculator, the approximate value of this expression is 11.7 cm.
Therefore, the slant height to the nearest tenth of a centimeter is B. 11.7 cm.
To find the slant height of a cone, we can use the formula:
\[L = \sqrt{r^2 + h^2}\]
Where L represents the slant height, r represents the radius, and h represents the height of the cone.
However, we are only given the lateral area of the cone, not the height. The lateral area of a cone can be calculated using the formula:
\[A = \pi \cdot r \cdot L\]
Where A is the lateral area, r is the radius, and L is the slant height.
Given that the lateral area is 555 cm² and the radius is 15.1 cm, we can rearrange the formula for lateral area to solve for the slant height:
\[L = \frac{A}{\pi \cdot r}\]
Substituting the given values:
\[L = \frac{555}{\pi \cdot 15.1}\]
Calculating this expression, we find that the slant height, L, is approximately 11.659 cm.
Since we need to round to the nearest tenth of a centimeter, the answer is B. 11.7 cm.