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Surface Areas and Volumes

Multiple Choice Questions

301. The volumes of two spheres are in the ratio 64 : 27. The ratio of their diameters is equal to:

4 : 3
3 : 4
16 : 9
16 : 9

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302. The curved surface area of a cone of slant height

straight x over 2

is πrx. Then area of its base is:

2m²
4πx²
πx²
πx²

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303. If the radius and height of a cone are both increased by 10%, then the volume of the cone is increased by:

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304. If the area of the base of a right circular cylinder is 38.5 cm² and its height is 6 cm, then its volume (in cm³) is:

231
115.5
462
462

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305. Area of base of a solid hemisphere is 36π cm². Then its volume is:

108 $straight pi$ cm³
72 $straight pi$ cm³
288 $straight pi$ cm³
288 $straight pi$ cm³

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306. Height of a cone is 12 cm and its base diameter is 10 cm. Its slant height is:

12.5 cm
313 cm
15 cm
15 cm

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307. If the sum of all the edges of a cube is 36 cm, then the volume of the cube is

9 cm³
27 cm³
216 cm³
216 cm³

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Short Answer Type

308. The radius of the base and the height of a right circular cone are 7 cm and 24 cm respectively. Find the volume and total surface area of the cone.

Here, r = 7 cm h = 24 cm

therefore

Volume of the cone =

Here, r = 7 cm h = 24 cm  Volume of the cone =

1 third πr squared straight h

equals 1 third cross times 22 over 7 cross times left parenthesis 7 right parenthesis squared cross times 24 equals space 1232 space cm cubed

and, total surface area of the cone = πr(l + r)

equals πr left parenthesis square root of straight r squared plus straight h squared space end root space plus straight r right parenthesis equals 22 over 7 cross times 7 cross times left parenthesis square root of left parenthesis 7 right parenthesis squared plus left parenthesis 24 right parenthesis squared end root plus 7 right parenthesis equals 22 cross times left parenthesis square root of 49 plus 576 end root plus 7 right parenthesis equals 22 cross times left parenthesis square root of 625 plus 7 right parenthesis equals 22 cross times left parenthesis 25 plus 7 right parenthesis equals 22 cross times 32 equals 704 space cm squared.

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309.

If the radius of the base of a right circular cone is halved keeping the height same, what is the ratio of the volume of the reduced cone to that of the original one?

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310. The base radii of the two right circular cones of the same height are in the ratio 3 : 5. Find the ratio of their volumes.

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