1.  The volume of a sphere of radius r is obtained by multiplying its surface area by :

43
r3
4r3
3r

```Answer

Answer: Option  B Explanation:Volume = 4⁄3 πr3 = r⁄3 (4πr2) = r⁄3 * Surface area. ```

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2.  The curved surface area of a right circular cylinder of base radius r is obtained by multiplying volume by :

2r
2r
2r2
2r2

```Answer

Answer: Option  B Explanation:Curved surface are = 2πrh = (πr2h) 2⁄r = (Volume * 2⁄r) ```

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3.  A hemisphere and a cone have equal bases. If their heights are also equal, then the ratio of their curved surfaces will be :

1 : 2
2 : 1
1 : $\sqrt{2}$
$\sqrt{2}$ : 1

```Answer

Answer: Option  D Explanation:Let the radius of each be R. Height of hemisphere, H = R.
So, height of cone = height of hemisphere = R.
Slant height of cone = $\sqrt{\mathrm{R2+ R2}}$ = $\sqrt{2}$R.
Curved surface area of hemisphere⁄Curved surface area of cone = 2πR2⁄πR * $\sqrt{2}$R = $\sqrt{2}$ : 1. ```

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4.  Surface area of a sphere is 2464 cm2. If its radius be doubled, then the surface area of the new sphere will be :

4928 cm2
9856 cm2
19712 cm2
Data insufficient

```Answer

Then, original surface area = 4πr2 = 2464 cm2 (given)
New surface area = 4π(2r)2 = 4 * 4πr2 = (4 * 2464) cm2 = 9856 cm2. ```

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5.  The dimensions of a piece of iron in the shape of a cuboid are 270 cm * 100 cm * 64 cm. If it is melted and recast into a cube. then the surface area of the cube will be :

14400 cm3
44200 cm3
57600 cm3
86400 cm3

```Answer

Answer: Option  D Explanation:Volume of the cube = (270 * 100 * 64) cm3.
Edge of the cube = $\sqrt{\mathrm{270 * 100 * 64}}$ cm = (3 * 10 * 4) cm = 120 cm.
Surface area = (6 * 120 * 120) cm2 = 86400 cm2. ```

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