Question

In the figure, from the top of a solid cone of height 12 cm and base radius 6 cm , a cone of height 4 cm is removed by a plane parallel to the base. Find the total surface area of the remaining solid

Answer 1

Answer:

Step-by-step explanation:

A cone of radius CD and height AD as shown in figure is cut from the top of 4cm at point E.

now, AD = 12cm , CD = 6cm , AE = 4cm

here it is clear that ∆ABE ~ ∆ACD

so, AE/AD = BE/CD

4cm/12cm = BE/6cm

BE = 2 cm { it is the radius of small circular part , Let r }

now, whole surface area of remaining part of cone = lateral surface area of frustum + area of above circular part + area of below circular part

= πl(R + r) + πr² + π R²

where, l = √{h² + (R - r)²}

here, h = 12cm - 4cm = 8 cm

so, l = √{8² + (6-2)²} = √{64 + 16} = 4√5cm

now, whole surface area = π × 4√5 × (6 +2) + π × (6)² + π × (2)²

= 32√5π + 36π + 4π cm²

= (32√5 + 40)π cm²

= (32 × 2.236 + 40) × 22/7 cm²

= 350.59 cm²

Answer 2

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