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The radius of a right circular cone is 2.1 cm and its height is 2.8 cm. The total surface area of the cone is: (Take π = 22/7)
23.1 cm2
46.2 cm2
18.48 cm2
36.96 cm2
36.96 cm2
Notice the Pythagorean triple (3, 4, 5) scaled by 0.7: (2.1, 2.8, 3.5). Thus, slant height l = 3.5. Total Surface Area = πr(r+l) = (22/7) * 2.1 * (2.1 + 3.5) = 22 * 0.3 * 5.6 = 6.6 * 5.6 = 36.96.
Radius of cone (r) = 2.1 cm, Height of cone (h) = 2.8 cm, Pi (π) = 22/7
TSA=πr(r+l)=πr(r+r2+h2)
Notice the Pythagorean triple (3, 4, 5) scaled by 0.7: (2.1, 2.8, 3.5). Thus, slant height l = 3.5. Total Surface Area = πr(r+l) = (22/7) * 2.1 * (2.1 + 3.5) = 22 * 0.3 * 5.6 = 6.6 * 5.6 = 36.96.
Students often use the height (h) instead of the slant height (l) in the total surface area formula, resulting in incorrect calculations.
Calculate Slant Height
Use the Pythagorean theorem to find the slant height l=r2+h2. Given r=2.1 and h=2.8, l=2.12+2.82.
l=4.41+7.84=12.25=3.5 cm
Apply Total Surface Area Formula
The formula for the total surface area of a cone is πr(r+l).
TSA=722×2.1×(2.1+3.5)
Final Calculation
Solve the arithmetic expression: TSA=722×2.1×5.6. Simplifying 2.1/7=0.3.
TSA=22×0.3×5.6=6.6×5.6=36.96 cm2
D is correct because the calculated total surface area of the cone is 36.96 cm².
Always look for Pythagorean triples in geometry problems involving cones, as they significantly simplify the calculation of the slant height.
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