Write your answer as an integer or as a decimal rounded to the nearest tenth
1 answer:
You might be interested in
The equation of the hyperbola is :
The center of a hyperbola is located at the origin that means at (0, 0) and one of the focus is at (-50, 0)
As both center and the focus are lying on the x-axis, so the hyperbola is a horizontal hyperbola and the standard equation of horizontal hyperbola when center is at origin:
The distance from center to focus is 'c' and here focus is at (-50,0)
So, c= 50
Now if the distance from center to the directrix line is 'd', then
Here the directrix line is given as : x= 2304/50
Thus,
⇒
⇒ a² = 2304
⇒ a = √2304 = 48
For hyperbola, b² = c² - a²
⇒ b² = 50² - 48² (By plugging c=50 and a = 48)
⇒ b² = 2500 - 2304
⇒ b² = 196
⇒ b = √196 = 14
So, the equation of the hyperbola is :
Answer:
The radius of the base of the cone is 2 units
The slant height of the cone is 4 units
The height of the cone is 2√3 units
The volume of the cone is units³
Step-by-step explanation:
* Lets revise the total surface area and the lateral area of a cone
- The lateral area of cone = π r l , where r is the radius of the base
and l is the slant height of the cone
- The surface area of the cone = π r l + π r², where π r l is the lateral
area and π r² is the base area
- The cone has three dimensions radius (r) , height (h) , slant height (l)
- r , h , l formed right triangle, r , h are its legs and l is its hypotenuse,
then l² = r² + h²
- The volume of the con = (π r² h)
* Now lets solve the problem
- We will use the total area to find the radius of the base
∵ TA = 12π
∵ TA = LA + πr²
∵ LA = 8π
- Substitute the value of the lateral area in the total area
∴ 12π = 8π + π r² ⇒ subtract 8π from both sides
∴ 12π - 8π = π r²
∴ 4π = π r² ⇒ divide both sides by π
∴ r² = 4 ⇒ take square root for both sides
∴ r = 2
* The radius of the base of the cone is 2 units
- We will use the lateral area to find the slant height
∵ LA = π r l
∵ LA = 8π
∵ r = 2
∴ π (2) l = 8π ⇒ divide both sides by π
∴ 2 l = 8 ⇒ divide both sides by 2
∴ l = 4
* The slant height of the cone is 4 units
- Use the rule l² = r² + h² to find the height of the cone
∵ r = 2 and l = 4
∵ l² = r² + h²
∴ (4)² = (2)² + h²
∴ 16 = 4 + h² ⇒ subtract 4 from both sides
∴ 12 = h² ⇒ take square root for both sides
∴ h = √12 = 2√3
* The height of the cone is 2√3 units
∵ The volume of the con = (π r² h)
∵ r = 2 and h = 2√3
∴ V = (π × 2² × 2√3) =
(π × 4 × 2√3) =
(π × 8√3)
∴ V =
* The volume of the cone is units³
