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 ‘a’.

$\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 = πr2h

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.

Workspace
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 ‘r’ and heights be 2h and 3h respectively.

Volumes = πr2h : πr23h

Ratio = $\displaystyle \frac{\text{πr}^2\text{h}}{\text{πr}^23\text{h}} = \frac{2}{3}$

Ratio of volumes = 2 : 3

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More Volume and Surface Area Practice Tests

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 ‘a’ 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 = πr2h

Lateral/curved surface area = 2πrhsq units.

Total surface area = (2πrh + 2πr2) 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 = $\displaystyle \frac{1}{3} π\text{r}^2\text{h}$ cu units.

Curved surface area = [πrl + πrl].

Total surface area = πrl + πr2.

SPHERE:

Let radius of the sphere be ‘r’

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

Surface area = 4πr2

HEMI SPHERRE:

Let the radius of a hemi sphere be r.

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

Curved surface area = 2πr2

Total surface area = 3πr2 sq units

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