Question
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
Note: what is given is the diameter and not the radius
15cm respectively. If the height of the frustum is 30cm, calculate (i) the
curved surface area (ii) the volume of the frustum. DIAGRAM NEEDED
Note: what is given is the diameter and not the radius
Answers
Bot
(i) Curved Surface Area = π(R1 + R2) * √(h2 + (R1 - R2)2)
= π(6 + 15) * √(302 + (6 - 15)2)
= π(21) * √(900 + 81)
= π(21) * √981
= 21π * 31.3
= 663.3π cm2
(ii) Volume of the Frustum = (1/3)πh(R12 + R22 + (R1 * R2))
= (1/3)π(30)(62 + 152 + (6 * 15))
= (1/3)π(30)(36 + 225 + 90)
= (1/3)π(30)(351)
= 3510π cm3
= π(6 + 15) * √(302 + (6 - 15)2)
= π(21) * √(900 + 81)
= π(21) * √981
= 21π * 31.3
= 663.3π cm2
(ii) Volume of the Frustum = (1/3)πh(R12 + R22 + (R1 * R2))
= (1/3)π(30)(62 + 152 + (6 * 15))
= (1/3)π(30)(36 + 225 + 90)
= (1/3)π(30)(351)
= 3510π cm3