10. The diagram below shows two similar flasks for measuring liquid.
Diagrams not drawn to scale
The flasks are in the shape of cones. The smaller flask has a base radius of 8 cm and a vertical height of 20 cm. The larger flask has a base radius of 14 cm.
(a)
Calculate the vertical height of the larger flask. [2]
(b)
The larger flask is now partly filled with liquid up to a vertical height of 15 cm.
Diagram not drawn to scale
Calculate the volume of liquid in the flask. Give your answer in terms of π. [4]
From the formula list: Volume of cone \(= \dfrac{1}{3}\pi r^2 h\)
Mark scheme (a)
Scheme
Marks
Comments
height = 14 × 20 ÷ 8 or 14 × 2·5 or equivalent
M1
Allow M1 for \(\dfrac{\text{height}}{14} = \dfrac{20}{8}\), OR \(\dfrac{\text{height}}{20} = \dfrac{14}{8}\)
Alternative methods: If candidates clearly work with similar volumes, then B1 for \(\tfrac{3}{4}\) or \(\tfrac{4}{3}\) or equivalent B1 for \(\left(\tfrac{3}{4}\right)^3\) or \(\left(\tfrac{4}{3}\right)^3\) or equivalent M1 for \(\tfrac{1}{3} \times \pi \times 8^2 \times 20 \times \left(\tfrac{3}{4}\right)^3\) or equivalent A1 for 180π (cm3)
OR
FT ‘their 35’ throughout B1 for \(\tfrac{15}{35}\) or \(\tfrac{35}{15}\) or equivalent B1 for \(\left(\tfrac{15}{35}\right)^3\) or \(\left(\tfrac{35}{15}\right)^3\) or equivalent M1 for \(\tfrac{1}{3} \times \pi \times 14^2 \times 35 \times \left(\tfrac{15}{35}\right)^3\) or equivalent A1 for 180π (cm3)
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