calculate the total surface area of a solid cone of slant height 15cm and base radius 8cm in terms of π

recall that the area is

A = πr(r+s)
Now plug in your numbers

Calculate in terms of π the total surface area of a solid cylinder of radius 3cm and height 4cm

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 = π × r × l,
where r is the radius of the base and l is the slant height.

Given:
Radius of the base (r) = 8 cm
Slant height (l) = 15 cm

Plugging in these values, we have:
LSA = π × 8 cm × 15 cm

2. Base Area (BA) of a cone:
The base area of a cone is given by the formula:
BA = π × r^2,
where r is the radius of the base.

Given:
Radius of the base (r) = 8 cm

Plugging in this value, we have:
BA = π × (8 cm)^2

3. Total Surface Area (TSA) of a cone:
The total surface area of the cone is the sum of the lateral surface area and the base area:
TSA = LSA + BA

Plugging in the values calculated above, we have:
TSA = (π × 8 cm × 15 cm) + (π × (8 cm)^2)

Simplifying the equation:
TSA = π × (8 cm × 15 cm + (8 cm)^2)

Calculating further:
TSA = π × (120 cm^2 + 64 cm^2)
TSA = π × (184 cm^2)

Therefore, the total surface area of the solid cone is 184π cm^2.

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

1. Lateral Surface Area of a cone:
The lateral surface area of a cone can be calculated using the formula πrl, where r is the radius of the base and l is the slant height.

In this case, the radius (r) is given as 8 cm and the slant height (l) is given as 15 cm.
So the lateral surface area of the cone is π * 8 * 15 (in terms of π).

Simplifying this, the lateral surface area of the cone is 120π square cm.

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

In this case, the radius (r) is given as 8 cm.
So the base area of the cone is π * 8^2 (in terms of π).

Simplifying this, the base area of the cone is 64π square cm.

3. Total surface area of the cone:
The total surface area of the cone is the sum of the lateral surface area and the base area.

Adding the lateral surface area (120π square cm) and the base area (64π square cm) gives:
Total surface area = 120π + 64π (in terms of π).

Simplifying this, the total surface area of the cone is 184π square cm.

Therefore, the total surface area of the given solid cone is 184π square cm.