12.5 Frustum of a Cone

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Step 1

  1. Identify Shape: Frustum.

Step 2

  1. Dimensions: h=14h = 14. d1=4  ⟹  r1=2d_1 = 4 \implies r_1 = 2. d2=2  ⟹  r2=1d_2 = 2 \implies r_2 = 1.

Step 3

  1. Formula: V=13πh(r12+r22+r1r2)V = \frac{1}{3} \pi h (r_1^2 + r_2^2 + r_1 r_2).

Step 4

  1. Substitute: V=13×227×14(22+12+2×1)V = \frac{1}{3} \times \frac{22}{7} \times 14 (2^2 + 1^2 + 2\times1).

Step 5

  1. Calculate: 443(4+1+2)=443(7)=3083≈102.67\frac{44}{3} (4+1+2) = \frac{44}{3} (7) = \frac{308}{3} \approx 102.67 cm³.
Final Answer

102.67 cm³

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