Find the volume of a frustum
10th grade (Year 11 in England) · 16 questions · Common Core: HSG.GMD.A.3, HSG.MG.A.1 · England: GCSE Higher Geometry
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Score/ 16
Question 1
A cone has base radius 12 cm and height 12 cm. The top is cut off parallel to the base, leaving a small cone of radius 6 cm and height 6 cm removed. Find the volume of the frustum that is left, to 1 decimal place.
Answer
Question 2
A cone of volume 576π cm³ has its top cut off. The removed cone is similar with a length scale factor of 2/3. What fraction of the original volume is left? Give a fraction.
Answer(as a fraction)
Question 3
A cone has base radius 12 cm and height 18 cm. The top is cut off parallel to the base, leaving a small cone of radius 4 cm and height 6 cm removed. Find the volume of the frustum that is left, to 1 decimal place.
Answer
Question 4
A cone of volume 486π cm³ has its top cut off. The removed cone is similar with a length scale factor of 1/3. What fraction of the original volume is left? Give a fraction.
Answer(as a fraction)
Question 5
A cone has base radius 12 cm and height 30 cm. The top is cut off parallel to the base, leaving a small cone of radius 4 cm and height 10 cm removed. Find the volume of the frustum that is left, to 1 decimal place.
Answer
Question 6
A cone of volume 720π cm³ has its top cut off. The removed cone is similar with a length scale factor of 2/3. What fraction of the original volume is left? Give a fraction.
Answer(as a fraction)
Question 7
A cone has base radius 18 cm and height 24 cm. The top is cut off parallel to the base, leaving a small cone of radius 9 cm and height 12 cm removed. Find the volume of the frustum that is left, to 1 decimal place.
Answer
Question 8
A cone of volume 405π cm³ has its top cut off. The removed cone is similar with a length scale factor of 2/3. What fraction of the original volume is left? Give a fraction.
Answer(as a fraction)
Question 9
A cone has base radius 6 cm and height 24 cm. The top is cut off parallel to the base, leaving a small cone of radius 3 cm and height 12 cm removed. Find the volume of the frustum that is left, to 1 decimal place.
Answer
Question 10
A cone of volume 144π cm³ has its top cut off. The removed cone is similar with a length scale factor of 2/3. What fraction of the original volume is left? Give a fraction.
Answer(as a fraction)
Question 11
A cone has base radius 18 cm and height 30 cm. The top is cut off parallel to the base, leaving a small cone of radius 6 cm and height 10 cm removed. Find the volume of the frustum that is left, to 1 decimal place.
Answer
Question 12
A cone of volume 180π cm³ has its top cut off. The removed cone is similar with a length scale factor of 1/3. What fraction of the original volume is left? Give a fraction.
Answer(as a fraction)
Question 13
A cone has base radius 6 cm and height 12 cm. The top is cut off parallel to the base, leaving a small cone of radius 2 cm and height 4 cm removed. Find the volume of the frustum that is left, to 1 decimal place.
Answer
Question 14
A cone of volume 486π cm³ has its top cut off. The removed cone is similar with a length scale factor of 2/3. What fraction of the original volume is left? Give a fraction.
Answer(as a fraction)
Question 15
A cone has base radius 12 cm and height 30 cm. The top is cut off parallel to the base, leaving a small cone of radius 4 cm and height 10 cm removed. Find the volume of the frustum that is left, to 1 decimal place.
Answer
Question 16
A cone of volume 180π cm³ has its top cut off. The removed cone is similar with a length scale factor of 2/3. What fraction of the original volume is left? Give a fraction.
Answer(as a fraction)
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