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Alenkasestr [34]
3 years ago
13

A frustum is formed when a plane parallel to a cone’s base cuts off the upper portion as shown. Which expression represents the

volume, in cubic units, of the frustum? π(7.52)(11) – π(3.52)(8) π(7.52)(11) + π(3.52)(8) π(7.52)(19) – π(3.52)(8) π(7.52)(19) + π(3.52)(8)

Mathematics
2 answers:
jeka943 years ago
7 0

Volume of Frustum having , H= 11 units, Larger radius (R)= 7.5 units , and Smaller radius(r) =3.5 units is given by=

 \frac{\pi\times H}{3} \times (R^2+R r+r^2)

Or, the volume of frustum can be calculated  by

= Volume of larger cone - volume of smaller cone

=\frac{\pi }{3}\times [(7.5)^2\times 19]-\frac{\pi }{3}\times [(3.5)^2\times 8]

As, total height= 11 +8=19 units, radius of smaller cone= 3.5 units

Radius of whole cone = 7.5 units

Option (C)

Bezzdna [24]3 years ago
3 0
Think of the two pieces together as a single cone of height 19, and its volume.
Then think of only the upper piece as a cone, and find its volume.
The volume of the frustum is the total volume minus the volume of the upper piece.

The volume of a cone is:

V = \dfrac{1}{3} \pi r^2 h

Total volume:

V_t = \dfrac{1}{3} \times \pi \times 7.5^2 \times 19

Volume of upper cone:

V_u = \dfrac{1}{3} \times \pi \times 3.5^2 \times 8

Volume of frustum:

V_f = \dfrac{1}{3}\pi(7.5^2)(19) - \dfrac{1}{3}\pi(3.5^2)(8)



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The picture in the attached figure

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