Answer:

1. Slant HEIGHT = 35 cm
2. Curved surface area = 2310 cm²
3. Total surface area = 3696 cm²

Step-by-step explanation:

Given that:

• Volume of a CONE = 12936 cm³
• Diameter of the base = 42 cm
• Then, Radius = Diameter/2 = 42/2 = 21 cm

Formula used:

1. V = (πr²h)/3 cubic unit
2. l = √(r² + h²) unit
3. CSA = πrl sq. unit
4. TSA = πr(r + l) sq. unit

Here,

• Volume of a cone = V
• Curved surface area of a cone = CSA
• Total surface area of a cone = TSA
• Slant height of a cone = l
• Radius of the base of a cone = r
• Height of a cone = H

Finding the height of the cone:

• Volume of a cone = (πr²h)/3 cubic unit
• 12936 = (22 × 21 × 21 × h)/(7 × 3)
• 12936 = 22 × 21 × h
• h = 12936/(22 × 21)
• h = 28

∴ Height of the cone = 28 cm

To Find:

1. Slant height
2. Curved surface area
3. Total surface area

Finding the slant height:

• Slant height = √(r² + h²) unit
• Slant height = √(21² + 28²) cm
• Slant height = √(441 + 784) cm
• Slant height = √1225 cm
• Slant height = 35 cm

Finding the curved surface area:

• Curved surface area = πrl sq. unit
• Curved surface area = (22 × 21 × 35)/7 cm²
• Curved surface area = 2310 cm²

Finding the total surface area:

• Total surface area = πr(r + l) sq. unit
• Total surface area = π × 21 × (21 + 35) cm²
• Total surface area = π × 21 × 56 cm²
• Total surface area = (22 × 21 × 56)/7 cm²
• Total surface area = 3696 cm²