Question
The radii of the ends of a frustum of a solid
right-circular cone 45 cm high are 28 cm and 7 cm. If this frustum is melted and reconstructed into a solid right circular cylinder whose radius of base and height are in the ratio 3 : 5, find the curved surface area (in cm²) of this cylinder. [Use π = 22/7.]Solution
Radius of cylinder =3x and height =5x The volume of the Frustum: V = 1/3 πh (R² + r² + Rr) = 1/3π×45× (72 + 282 +28×7)  = π ×15(49+784+196) = π ×15×1029 V=15435 π Volume of the Cylinder:  V = πr²h = 15435π π ×9x2×5x =15435 π 45x3=15435 x3=15435/45=343 x=7 r =3x =3×7= 21 cm, h =5x=5×7= 35 cm Curved Surface Area of the Cylinder: A = 2πrh = 2 × 22/ 7 x 21 x 35 =132×35 =4620 cm² Thus, the curved surface area of the cylinder is 4620 cm².
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