WORD PRBLEMS ON SURFACE AREA AND VOLUME

Problem 1 :

How many liters of milk can a hemispherical bowl of diameter 10.5 cm hold ?

Solution :

Capacity of the hemisphere = Volume of hemisphere

So, the capacity of the hemispherical bowl is 2.42 liters. 

Problem 2 :

Find the volume of the sphere whose surface area is 154 cm².

Solution :

Surface area of the sphere = 154 cm²

4πr² = 154

4(3.14)r² = 154

r² = 154/4(3.14)

r² = 12.26

r = 3.5

Volume of sphere = (4/3)πr³

= (4/3)(3.14)(3.5)³

= 179.5 cm³

So, volume of sphere is 179.5 cm³.

Problem 3 :

Find the capacity of the conical vessel (in liter) having height 8 cm and slant height 10 cm.

Solution :

Capacity of the conical vessel = volume of vessel

= (1/3) πr²h

h = 8 cm, l = 10 cm

l² = r² + h²

10² = r² + 8²

r² = 100 - 64

r² = 36

r = 6

Volume of the vessel = (1/3) π(6)²(8)

= 108π cm³

Volume of the conical vessel is 108π cm³.

Problem 4 :

Volume of two hemispheres are in the ratio 27 : 125. Find the ratio of the radii.

Solution :

Let r₁ and r₂ be the radii of two hemispheres.

Volume of hemisphere = (2/3) πr³

(2/3) πr₁³ : (2/3) πr₂³ = 27 : 125

r₁³ : r₂³ = 27 : 125

r₁³ : r₂³ = 3³ : 5³

r₁ : r₂= 3 : 5

So, ratio between the radii is 3 : 5.

Problem 5 :

The radius of the moon is approximately one fifth of the radius of the planet. Find the ratio of their volumes.

Solution :

Radius of the moon = 1/5 of radius of the planet

Let R be the radius of planet and r be the radius of moon

r = R/5

Volume of planet : Volume of moon

 (4/3) πR³ : (4/3) πr³

R³ : r³

R³ : (R/5)³

R³ : R³/125

125 : 1

Ratio between volume of planet to moon is 125 : 1.

Problem 6 :

Three cubes each with 8 cm edge are joined end to end. Find the total volume of the cuboid formed.

Solution :

Volume of cube = a³

= 8³ 

= 512

Volume of 3 cubes = 3(512)

= 1536 cm³

Volume of those cubes is 1536 cm³.

Problem 7 :

If the total surface area of cube is 726 cm², find its volume.

Solution :

Total surface area of cube = 6a²

6a² = 726

a² = 121

 a = 11

Volume of cube = a²

= (11)³

= 1331 cm³

So, volume of cube is 1331 cm^3.

Problem 8 :

A square plate is side x cm and 8 mm thick. If its volume is 22880 cm³ . Find the value of x.

Solution :

Volume = base area x height

base area = x²

height = 8 mm

1 cm = 10 mm

8 mm = 8/10 cm

volume = x² (0.8)

x² (0.8) = 22880

x² = 22880/0.8

x² = 28600

Use square roots on both sides.

x = 169.1 cm

Problem 9 :

The total surface area of solid cylinder is 616 cm² and radius is 7 cm, find the height.

Solution :

Total surface area of solid cylinder = 616 cm²

2πr (h + r) = 616

Applying r = 7 cm

2π(7) (h + 7) = 616

h + 7 = 616/14π

h + 7 = 616/44

h + 7 = 14

h = 14 - 7

h = 7 cm

So, the required height is 7 cm.

Problem 10:

Each face of cube has a perimeter of 32 cm. Find the volume of it.

Solution :

Each face of cube will be in the shape of square.

4a = 32

a = 8

Volume of cube = a³

= 8³

= 512 cm³