Find the height of a cone of area 550cm square and base radius 7cm square ,taking π to be 22/7.
I assume the lateral surface area = 550 cm^2
area = πrs, where s is the slant height
550 = π(7)s
s = 550/(7π) = 550/(7(22/7)) = 550/7 cm
h^2 = 7^2 + (550/22)^2 = 7^2 + 25^2
finish the arithmetic calculations
24 is the final answer
To find the height of a cone, we need to use the formula for the surface area of a cone and solve for the height.
The formula for the surface area of a cone is given by:
A = πrl + πr^2
Where:
A is the surface area
r is the base radius
l is the slant height
Given:
A = 550 cm^2
r = 7 cm
Now, we need to calculate the slant height (l) using the Pythagorean theorem.
The Pythagorean theorem states that:
l^2 = r^2 + h^2
Where:
h is the height of the cone
Rearranging the equation, we get:
h^2 = l^2 - r^2
Now, substitute the given values into the equation and solve for l:
h^2 = l^2 - (7 cm)^2
h^2 = l^2 - 49 cm^2
Next, substitute the formula for the surface area of a cone into the given surface area value:
550 cm^2 = πrl + πr^2
550 cm^2 = (22/7)(7 cm)(l) + (22/7)(7 cm)^2
550 cm^2 = 22l + 154 cm^2
Now, isolate the term with l:
22l = 550 cm^2 - 154 cm^2
22l = 396 cm^2
Divide both sides of the equation by 22:
l = 396 cm^2 / 22
l = 18 cm
Now, substitute the value of l into the equation for h^2:
h^2 = (18 cm)^2 - 49 cm^2
h^2 = 324 cm^2 - 49 cm^2
h^2 = 275 cm^2
Finally, take the square root of both sides to solve for h:
h = √(275 cm^2)
h ≈ 16.58 cm
Therefore, the height of the cone is approximately 16.58 cm.
To find the height of a cone, we can use the formula for the surface area of a cone:
A = πrl + πr²
Where A is the surface area, r is the radius of the base, and l is the slant height.
In this case, we are given that the surface area is 550 cm² and the base radius is 7 cm, and we are told to use π as 22/7.
Let's plug in the given values and solve for the slant height:
550 = (22/7)(7)(l) + (22/7)(7)²
550 = (22/7)(7l) + (22/7)(49)
550 = 22l + 22(7)
550 = 22l + 154
22l = 550 - 154
22l = 396
l = 396/22
l = 18
Now that we have the slant height (l) as 18 cm, we can find the height (h) using the Pythagorean theorem:
h² = l² - r²
h² = 18² - 7²
h² = 324 - 49
h² = 275
h = √275
h ≈ 16.58 cm
Therefore, the height of the cone is approximately 16.58 cm.