FINDING THE VOLUME OF 3D SHAPES

Volume of Prism, Cylinder, Cone or Sphere

Find the volume of the solid. If necessary, round your answer to the nearest whole number.

Problem 1 :

Solution :

By observing the figure, it is a rectangular prism.

Volume of the rectangular prism = length × Width × Height

We have,

Length = 9 in, Width = 4 in, and Height = 4 in

Volume = 9 × 4 × 4

= 144 in³

Problem 2 :

Solution :

By observing the figure, it is a triangular prism.

Volume of the triangular prism = Base area × Height

Length = 7 ft, Base = 6 ft, and Height = 10 ft

= 1/2 × 6 × 10 × 7

= 210  ft³

So, Volume of the triangular prisms is 210 ft³.

Problem 3 :

Solution :

By observing the figure, it is a cylinder.

Volume of the cylinder = πr²h

Given, Diameter (d) = 10 m, 

Radius (r) = d/2 = 10/2

Radius (r) = 5 m

Height of the cylinder = 7m.

Volume = (22/7) (5)² (7)

= 22 × 25

= 550 m³

So, volume of the cylinder is 550 m³.

Problem 4 :

Solution :

By observing the figure, it is a rectangular pyramid.

Volume of the rectangular pyramid = 1/3 × base area × Height

Length = 10 ft, Width = 10 ft, and Height = 12 ft

Volume = 1/3 × 10 × 10 × 12

V = 400 ft³

So, Volume of the pyramid is 400 ft³.

Problem 5 :

Solution :

By observing the figure, it is a Sphere.

Volume of the sphere = 4/3 πr³

Given, diameter (d) = 16 m

Radius (r) = d/2 = 16/2

r = 8 m

Volume = (4/3) (22/7) (8)³

= (4/3) (22/7) (512)

V = 2145 m³

So, volume of the sphere is 2145 m³.

Problem 6 :

Solution :

By observing the figure, it is a cone.

Volume of the cone = 1/3 πr²h

Radius (r) = 3 in, Height (h) = 5 in

Volume of the cone = (1/3) (22/7) (3)² (5)

= 330/7

V = 47 in³

So, Volume of the cone is 47 in³.

Problem 7 :

a) What is the volume of this standard size box of salt ?

b) What is the volume of the special offer box of salt, which is 20% bigger.

The standard size box contains enough salt to fill up 10 salt pots.

c) How many salt pots may be filed up from the special offer box of salt ?

Solution :

a) Volume of salt in the rectangular box = length x width x height

Length = 6 cm, width = 5 cm and height = 10 cm

= 6 x 5 x 10

= 300 cm³

b) volume of special offer box = 120% of 300

= 1.20(300)

 = 360 cm³

c) Quantity of salt in one pot = 300/10

= 30 cm³

Number of pots can be filled with special offer box = 360/30

= 12 boxes

Problem 8 :

Look at the triangle. Explain why x must be the right angle.

b) What is the volume of this prism ?

Solution :

a) Using Pythagorean theorem,

10² = 8² + 6²

100 = 64 + 36

100 = 100

Since Pythagorean theorem satisfies, it must be a right triangle.

b)

Volume of prism = base area x height

Area of triangle = (1/2) x 6 x 8

= 24 cm²

Volume of prism = 24 x 7

= 168 cm³

Problem 9 :

Prisms A and B have the same cross sectional area 

Copy and complete the table

Solution :

Cubes of ratio of side lengths = ratio of volume of prims.

Let x be the volume of prism B.

5 : 3  = 200 : x

5/3 = 200/x

5x = 200(3)

x = 40(3)

= 120 cm³

Problem 10 :

Tjs cat food is sold in this tins shaped like this. Each tin has an internal height 5 cm

The area of the lid of the tin is 35 cm². Workout the volume of cat food that the tin contains.

Solution :

Area of the lid = 35 cm²

Quantity of cat food = base area x height

= 35 x 5

= 175 cm³

Problem 11 :

Two solid spheres made of the same metal have weights 5920 g and 740 g, respectively. Determine the radius of the larger sphere, if the diameter of the smaller one is 5 cm.

Solution :

Let D be the diameter of large sphere.

D³ : 5³ = 5920 : 740

D³ : 5³ = 5920 : 740

D³ / 125 = 5920 / 740

D³ = (5920 / 740)(125)

D³ = 1000

D = 10

So, the diameter of the larger sphere is 10 cm.