alleryA metal cylinder (r=6 cm, h=8 cm) is melted into balls of radius 2 cm. How many?
- 18
- 27
- 36
- 24
Show answer and solution
Correct answer: B. 27
The cylinder volume is 288π and each sphere is 32π/3, giving 27 spheres.
ICSE Class 10 Mensuration: Surface Areas & Volumes — practice questions — page 2
Explore 65 free Mensuration: Surface Areas & Volumes questions in ICSE Class 10 Mathematics. Open each question or exercise to read its content, reference answers and available explanation.
Practise Mensuration: Surface Areas & Volumes with Quill →Mensuration: Surface Areas & Volumes questions and exercises with answers
Showing questions 31–60 of 65.
A metal cylinder (r=6 cm, h=8 cm) is melted into balls of radius 2 cm. How many?Read the answer and worked solution →A sphere of radius 6 cm is melted into a cylinder with radius 3 cm. Find cylinder height.Read the answer and worked solution →A pipe has outer radius 5 cm, inner radius 3 cm, and length 7 cm. Find material volume; π=22/7.Read the answer and worked solution →A cylindrical tank is 10 cm deep and has radius 3 cm. Find capacity; π=3.14.Read the answer and worked solution →A solid has a cylinder (r=3 cm, h=10 cm) and a hemisphere (r=3 cm) on top. Find volume in terms of π.Read the answer and worked solution →A cylinder (r=7 cm, h=10 cm) has a hemisphere of radius 7 cm on top. Find exposed area; π=22/7.Read the answer and worked solution →A cylindrical tank has radius 3 m and height 7 m. Find curved area using π=22/7.Read the answer and worked solution →How many cones of radius 3 cm and height 8 cm have the volume of one matching cylinder?Read the answer and worked solution →A closed cylinder has height equal to radius. Curved area:total area is?Read the answer and worked solution →A thin open-top cylinder has radius 3 cm,height 4 cm. Sheet area?Read the answer and worked solution →A pipe has radii 5,3 cm and length 2 cm. Its area, including both annular ends?Read the answer and worked solution →A radius-3 cm ball sinks fully in a radius-6 cm cylinder; no spill. Water rise?Read the answer and worked solution →Water from a full cylinder r=2,h=6 cm fills a right cone r=3 cm, no loss. Cone height?Read the answer and worked solution →Doubling a sphere's radius multiplies its volume by which factor?Read the answer and worked solution →A sphere is cut into two hemispheres. Total exposed area rises by?Read the answer and worked solution →For a solid hemisphere, curved area:total area equals?Read the answer and worked solution →A hemisphere has radius 3 cm. What is its volume?Read the answer and worked solution →Eight equal balls make one sphere, no loss. New radius:old ball radius?Read the answer and worked solution →A right cone and cylinder have equal heights and volumes. Cone radius:cylinder radius?Read the answer and worked solution →Equal-radius right cone and cylinder have equal curved areas. Slant height: cylinder height?Read the answer and worked solution →A sphere fits exactly in a closed cylinder. Sphere volume:cylinder volume?Read the answer and worked solution →A radius-3 cm hemisphere loses a coaxial cone of equal base and height. Volume left?Read the answer and worked solution →A radius-2 cm cylinder, length 5 cm, has hemispherical ends. External area?Read the answer and worked solution →Right cone r=3,slant=5 cm and radius-3 cm hemisphere join flat bases. Exposed area?Read the answer and worked solution →A cylinder r=3,h=4 cm has a right cone r=3,h=4 cm on top. Area including bottom?Read the answer and worked solution →A hollow sphere has outer radius 3 cm and inner radius 2 cm. Material volume?Read the answer and worked solution →A solid metal sphere has mass 288π g and density 8 g/cm³. Its radius?Read the answer and worked solution →No outflow: water rises 2 cm/min in a radius-7 cm cylinder. Inflow, π=22/7?Read the answer and worked solution →A cylinder's radius increases 20%; its height stays fixed. Volume increases by?Read the answer and worked solution →A cylinder's radius doubles while height halves. New volume:old volume?Read the answer and worked solution →
Worked practice questions
A sphere of radius 6 cm is melted into a cylinder with radius 3 cm. Find cylinder height.
- 36 cm
- 32 cm
- 24 cm
- 16 cm
Show answer and solution
Correct answer: B. 32 cm
Equal volumes give 4π(6³)/3 = π(3²)h, so h = 32 cm.
A pipe has outer radius 5 cm, inner radius 3 cm, and length 7 cm. Find material volume; π=22/7.
- 352 cm³
- 264 cm³
- 176 cm³
- 616 cm³
Show answer and solution
Correct answer: A. 352 cm³
Material volume = π(5²−3²)×7 = (22/7)×16×7 = 352 cm³.
How to practise
- Choose a Mensuration: Surface Areas & Volumes question and try to work out your answer.
- Open the question to check the correct answer and read its worked solution.
- Continue in the app for bite-sized lessons, explanations and review with Quill. You can start without creating an account.
Put it into practice
Continue with Mensuration: Surface Areas & Volumes practice for ICSE Class 10. Read explanations as you go. No signup form needed to start.
Practise Mensuration: Surface Areas & Volumes →