A right cone has a surface area of 628 cm squared and a diameter of 10cm what is the slant length

slant length = 35 cm

Step-by-step explanation:

A right cone has the vertex directly above the center of the base. The surface area of the right cone can be represented below.

surface area = πr (r + l)

where

r = radius

l = slant height/length

surface area = πr (r + l)

r = 10/2 = 5 cm

surface area = 628 cm²

Therefore,

628 = π * 5 (5 + l)

628 = 5π (5 + l)

628 = 25π + 5πl

628 = 25 * 3.14 + 5 * 3.14 * l

628 = 78.5 + 15.7l

628 - 78.5 = 15.7l

549.5 = 15.7l

divide both sides by 15.7

l = 549.5/15.7

l = 35 cm

slant length = 35 cm