Calculate the total surface area of a solid cone of

Base radius 6cm and slant height 10cm

Please help me solve it

To calculate the total surface area of a solid cone, we need to find the sum of the areas of the base and the lateral surface.

1. Base area:
The formula for the area of a circle is given by A = πr^2, where r is the radius.
Given that the base radius is 6 cm, we can substitute the value into the formula:
Base area = π(6 cm)^2

2. Lateral surface area:
The formula for the lateral surface area of a cone is given by A = πrl, where r is the radius and l is the slant height (or slant length).
Given that the radius is 6 cm and the slant height is 10 cm, we can substitute the values into the formula:
Lateral surface area = π(6 cm)(10 cm)

3. Total surface area:
Now, we can add the base area and the lateral surface area to find the total surface area of the cone:
Total surface area = Base area + Lateral surface area

Let's calculate the values step-by-step:

1. Base area:
Base area = π(6 cm)^2
Base area = π(36 cm^2)
Base area ≈ 113.1 cm^2 (rounded to one decimal place)

2. Lateral surface area:
Lateral surface area = π(6 cm)(10 cm)
Lateral surface area = π(60 cm^2)
Lateral surface area ≈ 188.5 cm^2 (rounded to one decimal place)

3. Total surface area:
Total surface area = Base area + Lateral surface area
Total surface area = 113.1 cm^2 + 188.5 cm^2
Total surface area ≈ 301.6 cm^2 (rounded to one decimal place)

Therefore, the total surface area of the solid cone is approximately 301.6 cm^2.

To calculate the total surface area of a solid cone, you need to find the lateral surface area and the base area and then add them together.

1. Lateral Surface Area (LSA) of a cone:
The lateral surface area of a cone can be found using the formula LSA = πrs, where r is the radius and s is the slant height.

Given:
- Base radius (r) = 6 cm
- Slant height (s) = 10 cm

Using the formula, LSA = πrs, we have:
LSA = π * 6 cm * 10 cm = 60π cm²

2. Base Area:
The base area of a cone can be found using the formula Base Area = πr², where r is the radius.

Given:
- Base radius (r) = 6 cm

Using the formula, Base Area = π * (6 cm)² = 36π cm²

3. Total Surface Area:
To find the total surface area, you need to add the lateral surface area and the base area together.

Total Surface Area = Lateral Surface Area + Base Area
Total Surface Area = 60π cm² + 36π cm²
Total Surface Area = 96π cm²

Therefore, the total surface area of the solid cone is 96π cm².

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