RV-26-001 · Similar cones: frustum capacity and material
A cone of radius 12 cm and height 52 cm has a smaller cone removed from its top by a cut parallel to the base. The removed cone has height 13 cm. The remaining frustum is inverted to make an open container, with its smaller circular end as the base.Diagram not accurately drawn
(a) Calculate the capacity of the container in litres, to 2 decimal places.
(b) Calculate the area of material needed for the curved surface and the smaller base. Give your answer to 2 decimal places. Use curved surface area of a frustum = π(R + r)s, where s is its slant height.
Part (a)Similar Cones (L.A.V) & Frustum Volume/Surface AreaBooklet p. 39, p. 40 & p. 41
Method
1) Put corresponding measurements in an L.A.V table (or L.L for two lengths)
2) Length factor r, area factor r², volume factor r³
3) Multiply from small to large; divide in reverse
Worked Example (RV-26-001 · Part (a))
Calculate the capacity of the container in litres, to 2 decimal places.
1)
Dimension
Small
Scale factor: small → large
Large
L (height)
13
4
52
L (radius)
3
4
12
V
31π(3)2(13)
(4)3
31π(12)2(52)
2)
Subtract cone volumes and convert cm³ to litres: 100031π[122(52)−(3)2(13)]=7.72 litres.
Ans =7.72 litres
Part (b)Similar Cones (L.A.V) & Frustum Volume/Surface AreaBooklet p. 39, p. 40 & p. 41
Method
1) Put corresponding measurements in an L.A.V table (or L.L for two lengths)
2) Length factor r, area factor r², volume factor r³
3) Multiply from small to large; divide in reverse
Worked Example (RV-26-001 · Part (b))
Calculate the area of material needed for the curved surface and the smaller base. Give your answer to 2 decimal places. Use curved surface area of a frustum = π(R + r)s, where s is its slant height.