Calculate the total surface area of a solid cone of vertical height 10cm and base diameter 14cm use the value 22/7 for
To calculate the total surface area of a solid cone, we need to consider the curved surface area of the cone and the area of the base.
The curved surface area (CSA) of a cone can be calculated using the formula:
CSA = π × r × l
where r is the radius of the base and l is the slant height of the cone.
The formula for the slant height (l) can be calculated using the Pythagorean theorem:
l = √(r^2 + h^2)
where h is the vertical height of the cone.
First, let's find the radius (r) of the base using the given base diameter of 14cm:
r = diameter / 2 = 14cm / 2 = 7cm
Next, let's find the slant height (l) using the given vertical height of 10cm and the radius we just calculated:
l = √(r^2 + h^2) = √(7^2 + 10^2) = √(49 + 100) = √149 = 12.21cm (approx.)
Now, we can plug in the values into the curved surface area formula:
CSA = π × r × l = (22/7) × 7cm × 12.21cm = 22 × 12.21 cm^2 = 268.62 cm^2 (approx.)
The area of the base of the cone is the area of a circle with radius r:
Area of base = π × r^2 = (22/7) × (7cm)^2 = 22 × 7^2 cm^2 = 22 × 49 cm^2 = 1078 cm^2
Finally, to find the total surface area, we add the curved surface area and the area of the base:
Total surface area = CSA + Area of base = 268.62 cm^2 + 1078 cm^2 = 1346.62 cm^2 (approx.)
Therefore, the total surface area of the solid cone is approximately 1346.62 cm^2.
To calculate the total surface area of a solid cone, we need to find the lateral surface area and add it to the base area.
First, let's find the slant height of the cone:
Using the Pythagorean theorem, we have:
(hypotenuse)^2 = (base)^2 + (height)^2
slant height^2 = radius^2 + height^2
The base diameter is given as 14 cm, so the radius is half of that, which is 7 cm.
Using the given height of 10 cm, we can calculate the slant height as follows:
slant height^2 = 7^2 + 10^2
slant height^2 = 49 + 100
slant height^2 = 149
Taking the square root of both sides gives us:
slant height = √149
Now, let's calculate the lateral surface area:
Lateral surface area = π * radius * slant height
Using the given value of 22/7 for π:
Lateral surface area = (22/7) * 7 * √149
Finally, let's calculate the base area:
Base area = π * radius^2
Base area = (22/7) * 7^2
Now we can calculate the total surface area by adding the lateral surface area to the base area:
Total surface area = Lateral surface area + Base area
You can substitute the values into the formulas above to calculate the total surface area of the cone.