Find the lateral surface area and total surface area of the cone that has a radius of 12 ft , slant height of 15 ft , and height of 9 ft .

To find the lateral surface area and total surface area of the cone, we can use the formulas: 1. Lateral Surface Area (LSA) of a cone: \[ LSA = \pi r l \] where: - \( r \) is the radius of the base of the cone - \( l \) is the slant height of the cone 2. Total Surface Area (TSA) of a cone: \[ TSA = LSA + \pi r^2 \] Given: - Radius of the base of the cone (\( r \)) = 12 ft - Slant height of the cone (\( l \)) = 15 ft - Height of the cone (\( h \)) = 9 ft We can calculate the lateral surface area and total surface area using the given values. Calculate the value by following steps: - step0: Calculate: \(\pi \times 12\times 15\) - step1: Multiply the terms: \(\pi \times 180\) - step2: Reorder the terms: \(180\pi \) The lateral surface area of the cone is approximately 565.49 square feet. Now, let's calculate the total surface area of the cone. Calculate the value by following steps: - step0: Calculate: \(\pi \times 12^{2}+180\pi \) - step1: Multiply the terms: \(144\pi +180\pi \) - step2: Collect like terms: \(\left(144+180\right)\pi \) - step3: Add the numbers: \(324\pi \) The total surface area of the cone is approximately 1017.88 square feet. Therefore, the lateral surface area of the cone is approximately 565.49 square feet, and the total surface area of the cone is approximately 1017.88 square feet.