Volume and Surface Area Questions

FACTS  AND  FORMULAE  FOR  VOLUME  AND  SURFACE  AREA  QUESTIONS

I. CUBOID

Let length=l, breadth =b and height =h units. Then,

1. Volume = (l x b x h)

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

3. Diagonal =$\sqrt{{l}^{2}+{b}^{2}+{h}^{2}}$ units

II. CUBE

Let each edge of a cube be of length a. Then,

1. Volume = ${a}^{3}$ cubic units.

2. Surface area = $6{a}^{2}$ sq.units

3. Diagonal = $\sqrt{3}a$ units

III. CYLINDER

Let radius of base = r and Height (or Length) = h. Then,

1.Volume = $\left({\mathrm{\pi r}}^{2}\mathrm{h}\right)$ cubic units

2. Curved surface area = $\left(2\mathrm{\pi }rh\right)$ sq.units

3. Total surface area = $\left(2\mathrm{\pi rh}+2{\mathrm{\pi r}}^{2}\right)$ sq.units

IV. CONE

Let radius of base =r and Height = h. Then,

1. Slant height, $l=\sqrt{{h}^{2}+{r}^{2}}$ units

2. Volume = $\left(\frac{1}{3}{\mathrm{\pi r}}^{2}\mathrm{h}\right)$ cubic units.

3. Curved surface area = $\left(\mathrm{\pi rl}\right)$sq.units

4. Total surface area = $\left(\mathrm{\pi rl}+{\mathrm{\pi r}}^{2}\right)$sq.units

V. SPHERE

Let the radius of the sphere be r. Then,

1. Volume =$\left(\frac{4}{3}{\mathrm{\pi r}}^{3}\right)$ cubic units

2. Surface area = $\left(4{\mathrm{\pi r}}^{2}\right)$ sq.units

VI. HEMISPHERE

Let the radius of a hemisphere be r. Then,

1. Volume = $\left(\frac{2}{3}{\mathrm{\pi r}}^{3}\right)$ cubic units.

2. Curved surface area = $\left(2{\mathrm{\pi r}}^{2}\right)$ sq.units

3. Total surface area = $\left(3{\mathrm{\pi r}}^{2}\right)$ sq.units

Q:

If each edge of a cube is increased by 50%, find the percentage increase in Its surface area

 A) 125% B) 150% C) 175% D) 110%

Explanation:

Let the edge = a cm

So increase by 50 % = a + a/2 = 3a/2

Total surface Area of original cube = $6a2$

TSA of new cube = $63a22$ =$69a24$=  $13.5a2$

Increase in area = $13.5a2-6a2$ =$7.5a2$

$7.5a2$ Increase % =$7.5a26a2×100$ = 125%

478 85359
Q:

A right triangle with sides 3 cm, 4 cm and 5 cm is rotated the side of 3 cm to form a cone. The volume of the cone so formed is:

 A) 12 pi cub.cm B) 15 pi cub.cm C) 16 pi cub.cm D) 20 pi cub.cm

Explanation:

105 51413
Q:

50 men took a dip in a water tank 40 m long and 20 m broad on a religious day. If the average displacement of water by a man is 4 cu.m , then the rise in the water level in the tank will be:

 A) 20 cm B) 25 cm C) 35 cm D) 50 cm

Explanation:

Total volume of water displaced =(4 x 50) cu.m = 200 cu.m

Rise in water level = $20040×20$=0.25m = 25cm

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Q:

A rectangular block 6 cm by 12 cm by 15 cm is cut up into an exact number of equal cubes. Find the least possible number of cubes.

 A) 30 B) 40 C) 10 D) 20

Explanation:

Volume of the block = (6 x 12 x 15) cu.cm = 1080 cu.cm

Side of the largest cube = H.C.F. of 6 cm, 12 cm, 15 cm

= 3 cm.

Volume of this cube  = (3 x 3 x 3) cu.cm = 27 cu.cm

Number of cubes =$108027$ = 40.

125 48622
Q:

A hall is 15 m long and 12 m broad. If the sum of the areas of the floor and the ceiling is equal to the sum of the areas of four walls, the volume of the hall is:

 A) 720 B) 900 C) 1200 D) 1800

Explanation:

86 39120
Q:

A cistern 6m long and 4 m wide contains water up to a depth of 1 m 25 cm. The total area of the wet surface is:

 A) 49 B) 50 C) 53.5 D) 55

Explanation:

Area of the wet surface = [2(lb + bh + lh) - lb]

= 2(bh + lh) + lb

= [2 (4 x 1.25 + 6 x 1.25) + 6 x 4]$m2$

= 49$m2$

85 38997
Q:

The diagonal of a rectangle is sqrt(41) cm.  and its area is 20 sq. cm. The perimeter of the rectangle must be:

 A) 9 cm B) 18 cm C) 20 cm D) 41 cm

Explanation:

$l2+b2$ = $diagonal2$=40

Also, lb=20

$l+b2=l2+b2+2lb$ = 41 + 40 =81

(l + b) = 9.

Perimeter = 2(l + b) = 18 cm.

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Q:

How many bricks each measuring 25cm x 11.25cm x 6cm, will be needed to build a wall 8m x 6m x 22.5m

 A) 5600 B) 600 C) 6400 D) 7200

Explanation:

No. of bricks= volume of the wall/volume of 1 brick

= (800 x 600 x 22.5) / (25 x 11.25 x 6) = 6400