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A sphere of maximum volume is cut out fr...

A sphere of maximum volume is cut out from a solid hemisphere. What is the ratio of the volume of the sphere to that of the remaining solid ?
किसी ठोस अर्धगोले से अधिकतम आयतन वाला एक गोला काटा जाता है | गोले के आयतन एवं शेष बचे ठोस के आयतन के बीच अनुपात ज्ञात करें |

A

`1 :4`

B

`1 :1`

C

`1 :2`

D

`1: 3`

Text Solution

Verified by Experts

The correct Answer is:
D
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A sphere of maximum volume is cut out from a solid hemisphere of radius r. The ratio of the volume of the hemisphere to that of the cut out sphere is: (a) 3:2 (b) 4:1 (c) 4:3 (d) 7:4

A right circular cylinder of maximum volume is cut out from a solid wooden cube. The material left is what percent of the volume (nearest to an integer) of the original cube ? एक ठोस लकड़ी के घन से अधिकतम आयतन वाला एक लम्ब वृत्तीय बेलन काटा जाता है | बची हुई सामग्री आरंभिक घन के आयतन (एक पूर्णाक के निकटतम ) का कितना प्रतिशत है ?

A sphere is inscribed in a cube. What is the ratio of the volume of the cube to the volume of the sphere? एक गोले को किसी घन में डाला गया है | घन के आयतन तथा गोले के आयतन में अनुपात ज्ञात करें |

A solid cube is cut into three cuboids of same volumes. What is the ratio of the surface area of the cube to the sum of the surface areas of any two of the cuboids so formed ? एक ठोस घन को समान आयतन वाले तीन घनाभों में काटा जाता है | घन के पृष्ठ क्षेत्रफल तथा किसी भी दो घनाभ के पृष्ठ क्षेत्रफलों के जोड़ के बीच अनुपात ज्ञात करें |

What is the volume of the sphere whose diameter is 42 cm? उस गोले का आयतन ज्ञात करें जिसका व्यास 42 सेमी है | (pi=22/7)

The volume of a sphere is 36 pi cm^3 . What is the radius of the sphere? एक गोले का आयतन 36 pi घन सेमी है | इस गोले की त्रिज्या ज्ञात करें |

The volume of a right circular cone is equal to that of a sphere, whose radius is half the radius of the base of the cone. What is the ratio of the radius of the base to the height of the cone ? एक लम्ब वृत्तीय शंकु का आयतन उस गोले के आयतन के बराबर है, जिसकी त्रिज्या शंकु के आधार की त्रिज्या से आधी है | शंकु के आधार की त्रिज्या और शंकु की ऊंचाई में क्या अनुपात है ?

If the radius of the base of a cone is doubled, and the volume of the new cone is three times the volume of the original cone, then what will be the ratio of the height of the original cone to that of the new cone ? यदि किसी शंकु के आधार की त्रिज्या दोगुनी कर दी गयी है , और नए शंकु का आयतन आरंभिक शंकु के आयतन का तिगुना है, तो आरंभिक शंकु और नए शंकु की ऊँचाइयों के बीच क्या अनुपात होगा ?

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