Question

The radius of the base of a cone is 5 cm and slant height is 9 cm. Find the total surface area of the cone​

Answer 1

To find the total surface area of a cone with a given radius and slant height, you need to calculate the lateral surface area and add it to the base area. The total surface area is the sum of these two areas which is 219.75 cm².

Step-by-step explanation:

To find the total surface area of a cone, we need to calculate the lateral surface area and add it to the base area. The lateral surface area of a cone can be calculated using the formula:

LSA = πrl

where r is the radius of the base and l is the slant height. In this case, r = 5 cm and l = 9 cm. Plugging these values into the formula, we get:

LSA = 3.142 × 5 cm × 9 cm = 141.21 cm²

The base area of a cone is given by the formula:

Base area = πr²

Plugging in the value of r = 5 cm, we get:

Base area = 3.142 × (5 cm)² = 78.54 cm²

To find the total surface area, we add the lateral surface area and the base area:

Total surface area = LSA + Base area = 141.21 cm² + 78.54 cm² = 219.75 cm²

Answer 2

To find the total surface area of a cone, we need to add the area of the base to the lateral surface area. The lateral surface area of a cone is the curved surface area that makes up the slanted sides of the cone.

The formula for the lateral surface area of a cone is given by:

Lateral surface area of cone = πrℓ

where r is the radius of the base of the cone and ℓ is the slant height.

Here, the radius of the base is 5 cm and the slant height is 9 cm.

So, the lateral surface area of the cone is:

Lateral surface area = πrℓ

= π × 5 × 9

= 45π cm²

The formula for the area of the base of a cone is:

Area of base of cone = πr²

where r is the radius of the base.

Here, the radius of the base is 5 cm.

So, the area of the base of the cone is:

Area of base = πr²

= π × 5²

= 25π cm²

Therefore, the total surface area of the cone is:

Total surface area = Lateral surface area + Area of base

= 45π + 25π

= 70π cm²

So, the total surface area of the cone is 70π cm².