Common Core HSG.MG.A.1 worksheet
High school · 16 questions · Common Core: HSG.GMD.A.3, HSG.MG.A.1 · England: GCSE Higher Geometry
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Question 1
A capsule is a cylinder of radius 8 cm and length 13 cm with a hemisphere on one end. Find its volume to 1 decimal place.
Answer
Question 2
A rocket model is a cylinder (radius 6 cm, height 13 cm) with a cone (same radius, height 8 cm) on top. Find its volume to 1 decimal place.
Answer
Question 3
A cone of volume 864π 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 4
A cone with the same base and height is drilled out of a solid cylinder (radius 6 cm, height 13 cm). Give the exact remaining volume as a multiple of π.
Answer
Question 5
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 3 cm and height 6 cm removed. Find the volume of the frustum that is left, to 1 decimal place.
Answer
Question 6
A capsule is a cylinder of radius 7 cm and length 13 cm with a hemisphere on one end. Find its volume to 1 decimal place.
Answer
Question 7
A rocket model is a cylinder (radius 7 cm, height 5 cm) with a cone (same radius, height 8 cm) on top. Find its volume to 1 decimal place.
Answer
Question 8
A cone of volume 216π 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 with the same base and height is drilled out of a solid cylinder (radius 7 cm, height 5 cm). Give the exact remaining volume as a multiple of π.
Answer
Question 10
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 6 cm and height 9 cm removed. Find the volume of the frustum that is left, to 1 decimal place.
Answer
Question 11
A capsule is a cylinder of radius 6 cm and length 13 cm with a hemisphere on one end. Find its volume to 1 decimal place.
Answer
Question 12
A rocket model is a cylinder (radius 8 cm, height 14 cm) with a cone (same radius, height 9 cm) on top. Find its volume to 1 decimal place.
Answer
Question 13
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 14
A cone with the same base and height is drilled out of a solid cylinder (radius 9 cm, height 6 cm). Give the exact remaining volume as a multiple of π.
Answer
Question 15
A cone has base radius 6 cm and height 30 cm. The top is cut off parallel to the base, leaving a small cone of radius 4 cm and height 20 cm removed. Find the volume of the frustum that is left, to 1 decimal place.
Answer
Question 16
A capsule is a cylinder of radius 3 cm and length 9 cm with a hemisphere on one end. Find its volume to 1 decimal place.
Answer
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