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What is the surface area of a cone with a lateral height of 1010 inches, a diameter of 1212 inches, and a height of 88 inches

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Full solution

Q. What is the surface area of a cone with a lateral height of 1010 inches, a diameter of 1212 inches, and a height of 88 inches
  1. Calculate Radius: Calculate the radius of the base of the cone.\newlineThe diameter of the cone is given as 1212 inches. The radius is half of the diameter.\newlineRadius (r)=Diameter2=12 inches2=6 inches(r) = \frac{\text{Diameter}}{2} = \frac{12 \text{ inches}}{2} = 6 \text{ inches}
  2. Calculate Slant Height: Calculate the slant height ll of the cone.\newlineThe lateral height, also known as the slant height, is given as 1010 inches. Therefore, we do not need to calculate it.\newlineSlant height ll = 1010 inches
  3. Calculate Surface Area: Calculate the surface area of the cone.\newlineThe surface area (SA) of a cone is given by the formula SA=πr(l+r)SA = \pi r(l + r), where rr is the radius of the base and ll is the slant height.\newlineSA=π×6SA = \pi \times 6 inches ×(10\times (10 inches +6+ 6 inches)=π×6) = \pi \times 6 inches ×16\times 16 inches\newlineSA=96πSA = 96\pi square inches

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