Calculate the total surface area of the solid cone or vertical height 24cm and base diameter 14cm use the value 22/7 for pier
TSA=πrl+πr²=πr(l+r)......(1)
l=√(h²+r²)......(2)
Where r=7 h=24
Plug r and h into equation (2) and finish it off at equation (1)
Total surface area of a solid cone of slant height 25 cm and vertical height 24cm.
We can start by using the formula for the surface area of a cone:
TSA = πrℓ + πr^2
where r is the radius of the base and ℓ is the slant height.
We know that the vertical height of the cone is 24 cm and the slant height is 25 cm. We can use the Pythagorean theorem to find the radius of the base:
r = √(ℓ^2 - h^2) = √(25^2 - 24^2) ≈ 7.0 cm
Now we can plug in the values for r and ℓ into the formula for the surface area:
TSA = π(7.0)(25) + π(7.0)^2 ≈ 615.75 cm^2
Therefore, the total surface area of the solid cone is approximately 615.75 cm^2.
Oh, a cone! That sounds fun! So, let's calculate its total surface area, shall we?
First, we need to find the slant height of the cone. To do that, we can use the Pythagorean theorem. The vertical height (h) is given as 24 cm, and the base diameter (d) is 14 cm.
The radius (r) is half of the diameter, so r = 14 cm / 2 = 7 cm.
Now, let's calculate the slant height using the Pythagorean theorem:
slant height (l) = √(r^2 + h^2)
= √(7^2 + 24^2)
= √(49 + 576)
= √625
= 25 cm
Now that we have the slant height, we can calculate the total surface area (TSA) of the cone. The formula for TSA is:
TSA = πr(r + l)
Plugging in the values we know:
TSA = (22/7) * 7 (7 + 25)
= (22/7) * 7 * 32
= (22/1) * 32
= 704 cm^2
So, the total surface area of the cone is 704 cm^2. Now, wasn't that cone-siderably funny?
To calculate the total surface area of a solid cone, you need to consider two parts: the curved surface area and the base area.
First, let's find the curved surface area of the cone. The curved surface area is the lateral surface area of the cone and can be calculated using the formula:
Curved Surface Area = π * r * l
Where π is the mathematical constant approximately equal to 3.14159, r is the radius of the base, and l is the slant height of the cone.
We are given the diameter of the base as 14 cm, which means the radius (r) is half of that, so r = 14/2 = 7 cm.
To find the slant height (l) of the cone, we can use the Pythagorean theorem. The slant height, height (h), and radius (r) together form a right triangle. Given the height (vertical height) of the cone as 24 cm, we can find the slant height (l) using the following equation:
l = √(r^2 + h^2)
Plugging in the values, we have:
l = √(7^2 + 24^2)
= √(49 + 576)
= √625
= 25 cm
Now we can calculate the curved surface area:
Curved Surface Area = π * 7 * 25
= 175π cm^2
Next, let's find the base area of the cone. The base area can be found using the formula:
Base Area = π * r^2
Plugging in the value of the radius (r = 7 cm), we have:
Base Area = π * 7^2
= 49π cm^2
Finally, to find the total surface area, we add the curved surface area and the base area:
Total Surface Area = Curved Surface Area + Base Area
= 175π + 49π
= 224π cm^2
As the question asks to use the value 22/7 for π, we can further simplify the result:
Total Surface Area ≈ 224 * (22/7)
≈ 704 cm^2
So, the total surface area of the solid cone is approximately 704 cm^2.