The diameters of the top and bottom of a frustum of a cone are 6cm and 15cm respectively. If the height of the frustum is 30cm, calculate (i) the curved surface area (ii) the volume of the frustum. (DIAGRAM NEEDED )

(i) Curved Surface Area = π(6 + 15) × √(225 + 36) = 441.7 cm²

(ii) Volume of Frustum = 1/3 × π × 30 × (6² + 6 × 15 + 15²) = 1150 cm³

Did you know?

Did you know that a frustum of a cone is a shape formed by cutting off the top of a cone with a plane parallel to its base? In this case, with diameters of 6cm and 15cm at the top and bottom, and a height of 30cm, we can calculate its curved surface area and volume. To calculate the curved surface area, we need to find the slant height of the frustum first using the Pythagorean theorem. Once we have the slant height, we can calculate the curved surface area by multiplying it with the average of the diameters. For the volume, we can use the formula: 1/3 * π * (R^2 + r^2 + R*r) * h, where R and r are the radii of the top and bottom of the frustum, and h is the height. So, with this information, we can calculate both the curved surface area and volume of the frustum of the cone.