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 ) . Please with solution
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(i) Curved Surface Area = π(R1 + R2) × √(R1 - R2)² + h²
= π(6 + 15) × √(6 - 15)² + 30²
= π × 21 × √(9 + 900)
= π × 21 × √909
= π × 21 × 30.1
= 2037.1π cm²
(ii) Volume of the Frustum = (1/3) × π × h × (R1² + R1 × R2 + R2²)
= (1/3) × π × 30 × (6² + 6 × 15 + 15²)
= (1/3) × π × 30 × (36 + 90 + 225)
= (1/3) × π × 30 × 351
= 3510π cm³