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A right circular cone of base radius 15 cm and height 40 cm is cut parallel to its base so as to obtain a frustum of height 10 cm and volume of 2000π cm3. What is the radius of the upper base of the frustum?1). 8 cm2). 9 cm3). 10 cm4). 12 cm |
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Answer» Let the radius of the upper base of the frustum be ‘r’ cm Now, ⇒ Volume of CONE = (1/3) × π × (base radius)2 × height ⇒ Volume of cone before cutting = (1/3) × π × (15)2 × 40 = 3000π cm3 Now, when a cone is cut parallel to its base, the base part is the frustum and the remaining part is ALSO a cone, whose base radius is equal to the radius of the upper base of the frustum ⇒ Base radius of remaining cone = r cm As, ⇒ Volume of frustum = 2000π cm3 ⇒ Volume of other cone = 3000π – 2000π = 1000π cm3 Also, ⇒ Height of other cone = 40 – 10 = 30 cm According to the question, ⇒ 1000π = (1/3) × π × (r)2 × 30 ⇒ r2 = 100 ⇒ r = √100 = 10 cm ∴ Radius of upper base of frustum = 10 cm |
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