If the surface area of the cone is 15 π and the center angle of the side view is 60 °, the volume of the cone will be smaller Detailed explanation: if the radius of the cone bottom is r, the perimeter of the cone bottom is 2 π R. if the center angle of the side view is 60 °, the arc length of the sector is 2 π R, and the radius of the sector is l, then 60 π L / 180 = 2 π R, l = 6R, the area of the sector is 2 π R × 6R / 2 = 6 π R & # 178; the surface area of the cone is 15 π = the bottom area + the area of the sector = π R & # 178; + 6 π R & # 178; = 7 π R & # 178;, R & # 178; = 15 / 7, r = √ 105 / 7, and the generatrix length of the cone is 6R, According to Pythagorean theorem, the height of the cone is √ 35r, and the volume of the cone is π R & # 178; × √ 35r / 3 = 25 π √ 3 / 7 π R & # 178; × √ 35r / 3 = 25, π √ 3 / 7 is wool?

If the surface area of the cone is 15 π and the center angle of the side view is 60 °, the volume of the cone will be smaller Detailed explanation: if the radius of the cone bottom is r, the perimeter of the cone bottom is 2 π R. if the center angle of the side view is 60 °, the arc length of the sector is 2 π R, and the radius of the sector is l, then 60 π L / 180 = 2 π R, l = 6R, the area of the sector is 2 π R × 6R / 2 = 6 π R & # 178; the surface area of the cone is 15 π = the bottom area + the area of the sector = π R & # 178; + 6 π R & # 178; = 7 π R & # 178;, R & # 178; = 15 / 7, r = √ 105 / 7, and the generatrix length of the cone is 6R, According to Pythagorean theorem, the height of the cone is √ 35r, and the volume of the cone is π R & # 178; × √ 35r / 3 = 25 π √ 3 / 7 π R & # 178; × √ 35r / 3 = 25, π √ 3 / 7 is wool?

The surface area of cone = side area + bottom area, side area = π × generatrix radius, bottom area = π × radius & # 178; because: the center angle of circle is 60 °, so: generatrix: radius = 360 ° / 60 ° = 6:1 now let radius be r, then generatrix is 6R, so: π × 6R × R + π × R & # 178; = 15 π 7 π R & # 178; = 15 π R & #