alleryWhat height gives a right cone of radius r the volume of a radius-r hemisphere?
- Height 3r
- Height 2r
- Height r
- Height 4r
Show answer and solution
Correct answer: B. Height 2r
Equating πr²h/3 to 2πr³/3 gives h = 2r.
ICSE Class 10 Mensuration: Surface Areas & Volumes — practice questions — page 3
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.
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Showing questions 61–65 of 65.
What height gives a right cone of radius r the volume of a radius-r hemisphere?Read the answer and worked solution →A cylinder has volume 1540 cm³ and curved area 440 cm². Its radius?Read the answer and worked solution →A sphere's surface area divided by volume is 1 cm⁻¹. Its radius?Read the answer and worked solution →A right cone has radius 5 cm and slant height 13 cm. Its vertical height?Read the answer and worked solution →A cylinder r=3,h=8 cm loses 1/9 volume on recasting into radius-2 cm balls. Number?Read the answer and worked solution →
Worked practice questions
A cylinder has volume 1540 cm³ and curved area 440 cm². Its radius?
- 3.5 cm
- 10 cm
- 14 cm
- 7 cm
Show answer and solution
Correct answer: D. 7 cm
Dividing volume by curved area gives r/2 = 3.5 cm, so r = 7 cm.
A sphere's surface area divided by volume is 1 cm⁻¹. Its radius?
- 2 cm
- 4 cm
- 3 cm
- 1 cm
Show answer and solution
Correct answer: C. 3 cm
The surface-area-to-volume ratio is 3/r, so r = 3 cm.
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