## Volume and Surface Area Questions - 1

Volume of a cube is 1728 cu.cm, then the length of the side is ?
• 18 cm
• 16 cm
• 13 cm
• 12 cm
• 8 cm
Explanation

Volume of a cube = side3 or a3, where "a" is side or edge.

Side = $\displaystyle \sqrt[3]{1728}$ = 12 cm, i.e cube root of 1728 is 12.

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Diagonal of a cube is $\displaystyle \sqrt{675}$ cm, then volume of the cube is ?
• 2835 cu.cm
• 4215 cu.cm
• 1325 cu.cm
• 3125 cu.cm
• 3375 cu.cm
Explanation

Diagonal of a cube = $\displaystyle \sqrt{3} \times$ side.

Let side of the cube be â€˜aâ€™.

$\displaystyle \sqrt{3} \times$ a = $\displaystyle \sqrt{675}$ = a = $\displaystyle \frac{\sqrt{675}}{\sqrt{3}} = \sqrt{225}$ = 15.

Side = 15 cm; Volume = side3 = 153 = 3375 cu.cm.

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Total surface area and lateral surface area, of a cube of side 18 cm respectively is ?
• 1836 sq.cm, 1484 sq.cm
• 1484 sq.cm, 1836 sq.cm
• 1944 sq.cm, 1296 sq.cm
• 1944 sq.cm, 1484 sq.cm
• 1296 sq.cm, 1944 sq.cm
Explanation

Total surface area of a cube = 6 a2

Total surface area = 6 x 182 = 6 x 324 = 1944 sq.cm.

Lateral surface area = 4 a2 = 4 x 324 = 1296 sq.cm.

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Length and Breadth and Height of a cuboid are 8 cm, 6 cm and 4 cm respectively, find total surface area ?
• 196 sq.cm
• 208 sq.cm
• 192 sq.cm
• 208 cu.cm
• 192 cu.cm
Explanation

Total surface area of a cuboid = 2(lb + bh + lh)

l = 8 cm, b = 6 cm, h = 4 cm.

Total surface area = 2(8 x 6 + 6 x 4 + 8 x 4).

=> 2(48 + 24 + 32) = 2(104) = 208 sq.cm.

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Find lateral/curved surface area of a cuboid measuring 6 cm in length, 4 cm in breadth and 2 $\displaystyle \frac{1}{2}$ cm in height ?
• 64 sq.cm
• 36 sq.cm
• 48 sq.cm
• 50 sq.cm
• 49 sq.cm
Explanation

Lateral surface area of a cuboid = 2h ( l + b ).

h = 2.5 cm; l = 6 cm; b = 4 cm.

Lateral surface area = 2 x 2.5 ( 6 + 4 ) = 5 ( 10 ) = 50 sq.cm.

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A brick measures 16 cm, 12 cm and 10 cm, how many bricks will be required for a wall 60 meter long, 1 $\displaystyle \frac{1}{2}$ meter high, and $\displaystyle \frac{1}{5}$ meter thick ?
• 11125
• 12845
• 13225
• 9825
• 9375
Explanation

Volume of each brick = 16 x 12 x 10 = 1920 cu.cm.

Volume of the wall = 60 meters = 6000 cm, height = 1 $\displaystyle \frac{1}{2}$ meter = 1.5 meter or 150 cm.

Thick = $\displaystyle \frac{1}{5}$ meter or 20 cm.

Number of bricks required = $\displaystyle \frac{\text{Volume of wall}}{\text{Volume of brick}} = \frac{6000 \times 150 \times 20}{1920}$ = 9375.

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A cube of side 6 cm is melted and a smaller cubes of side 2 cm each are formed, how many such cubes are formed ?
• 18
• 36
• 27
• 8
• 64
Explanation

Number of cubes so formed = $\displaystyle \frac{\text{Volume of the original cube}}{\text{Volume of the smaller cube}} = \frac{6^3}{2^3} = \frac{216}{8}$ = 27.

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A rectangular block measuring 12 cm, 18 cm and 24 cm is cut up into exact number of equal cubes the least possible number of cubes will be ?
• 18
• 24
• 36
• 27
• 81
Explanation

Volume of the block = 12 x 18 x 24 = 5184 cu.cm.

HCF of 12, 18 and 24 is 6 or 6 cm.

Volume = 6 x 6 x 6 = 216 cu.cm.

Number of cubes = $\displaystyle \frac{5184}{216}$ = 24.

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Find volume of a cylinder if diameter of the base is 14 cm and its height is 14 cm ?
• 1728 cu.cm
• 1296 cu.cm
• 3216 cu.cm
• 2186 cu.cm
• 2156 cu.cm
Explanation

Volume of a cylinder = Ï€r2h

Radius = $\displaystyle \frac{\text{Diameter}}{2} = \frac{14}{2}$ = 7 cm.

Volume = $\displaystyle \frac{22}{7} \times 7 \times 7 \times 14$ = 2156 cu.cm.

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Heights of two cylinders are in the ratio 2 : 3, with equal base then ratio between the volumes is ?
• 2 : 3
• 8 : 27
• 4 : 9
• 1 : 2
• 8 : 15
Explanation

Let radius of the cylinder be â€˜râ€™ and heights be 2h and 3h respectively.

Volumes = Ï€r2h : Ï€r23h

Ratio = $\displaystyle \frac{\text{Ï€r}^2\text{h}}{\text{Ï€r}^23\text{h}} = \frac{2}{3}$

Ratio of volumes = 2 : 3

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## Volume and Surface Area Formulas

### CUBOID:

Length = l, Breadth = b, Height = h.

Volume: l x b x h cu.units.

Lateral surface area = 2h( l + b ).

Surface area = 2 (lb + bh + lh).

Diagonal = $\displaystyle \sqrt{\text{l}^2 + \text{b}^2 + \text{h}^2}$

### CUBE:

Let each length edge of a cube be a

Length â€˜aâ€™ then,

Volume = a3

Lateral surface area = 4a2

Total surface area = 6a2

Diagonal = $\displaystyle \sqrt{3}$ a units.

### CYLINDER:

Let radius of the base = r

Height or length = h

Volume = Ï€r2h

Lateral/curved surface area = 2Ï€rhsq units.

Total surface area = (2Ï€rh + 2Ï€r2) sq units.

### CONE:

Let the radius of the base be r,

Height be h,

Slant height = l = $\displaystyle \sqrt{\text{h}^2 + \text{r}^2}$

Volume = $\displaystyle \frac{1}{3} Ï€\text{r}^2\text{h}$ cu units.

Curved surface area = [Ï€rl + Ï€rl].

Total surface area = Ï€rl + Ï€r2.

### SPHERE:

Let radius of the sphere be â€˜râ€™

Volume = $\displaystyle \frac{4}{3} Ï€\text{r}^3$   cu. Units.

Surface area = 4Ï€r2

### HEMI SPHERRE:

Let the radius of a hemi sphere be r.

Volume = $\displaystyle \frac{2}{3} Ï€\text{r}^3$

Curved surface area = 2Ï€r2

Total surface area = 3Ï€r2 sq units

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