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The radius and slant height of a cone are 59.5 cm and 85 cm, respectively. Find its total surface area. (Take π=722)
27489 cm²
27589 cm²
27499 cm²
27689 cm²
27499 cm²
Use the unit digit and digital sum: 22/7×59.5=22×8.5=187. Then 187×(59.5+85)=187×144.5. Ending digit: 7×5 ends in .5, which filters out options without .5.
Radius r = 59.5 cm, Slant height l = 85 cm, value of π=22/7.
TSA=πr(r+l)
Use the unit digit and digital sum: 22/7×59.5=22×8.5=187. Then 187×(59.5+85)=187×144.5. Ending digit: 7×5 ends in .5, which filters out options without .5.
Confusing Total Surface Area of a cone (πr(r+l)) with Curved Surface Area (πrl), or miscalculating the decimal multiplication.
Identify the formula
The total surface area of a cone is given by the sum of its curved surface area and base area.
TSA=πrl+πr2=πr(l+r)
Substitute the given values
Substitute r=59.5 and l=85 with π=22/7.
TSA=722×59.5×(85+59.5)
Calculate the intermediate steps
Simplify the expression: 59.5/7=8.5. Thus, 22×8.5=187. Then, 187×144.5.
TSA=187×144.5
Final calculation
Perform the multiplication 187×144.5=27021.5.
TSA=27021.5 cm2
C is correct because the calculated total surface area of the cone is 27,021.5 cm2.
Remember that for any circular geometry problem involving π=22/7, look for values divisible by 7 to simplify calculations quickly.
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