To get the best deal on Tutoring, call 1-855-666-7440 (Toll Free)

Volume of Pyramids and Cones Worksheet - Page 2

Volume of Pyramids and Cones Worksheet
  • Page 2
 11.  
If the side of each cube in the shown pyramid is 4 cm, then find the total volume occupied by the cubes.

a.
7676 cm3
b.
7670 cm3
c.
7680 cm3
d.
7665 cm3


Solution:

Assume the pyramid as the layers of cubes.

Number of cubes in the first layer = 8 + 7 + 6 + 5 + 4 + 3 + 2 + 1 = 36

Number of cubes in the second layer = 7 + 6 + 5 + 4 + 3 + 2 + 1 = 28

Number of cubes in the third layer = 6 + 5 + 4 + 3 + 2 + 1 = 21

Number of cubes in the fourth layer = 5 + 4 + 3 + 2 + 1 = 15

Number of cubes in the fifth layer = 4 + 3 + 2 + 1 = 10

Number of cubes in the sixth layer = 3 + 2 + 1 = 6

Number of cubes in the seventh layer = 2 + 1 = 3

Number of cubes in the eighth layer = 1

So, total number of cubes in the pyramid = 36 + 28 + 21 + 15 + 10 + 6 + 3 + 1 = 120

Volume of each cube = 64 cm3
[Side of each cube = 4 cm.]

The volume occupied by the cubes of the pyramid = Total number of cubes × volume of each cube = 120 × 64 = 7680 cm 3


Correct answer : (3)
 12.  
Find the volume of a cone and round the answer to the nearest whole unit.

a.
2366.3 in3
b.
2366 in3
c.
2365 in3
d.
2377 in3


Solution:

Volume of a cone, V = 13 π r2 h
[Formulae.]

= 13 × 3.141 × 10.5 × 10.5 × 20.5
[ r =10.5; h = 20.5 and substituting the values.]

= 2366.3 in.3 = 2366 in.3
[ Simplify and round the answer to the nearest whole unit.]

The volume of the cone to the nearest whole unit is 2366 in.3.


Correct answer : (2)
 13.  
Find the volume of a cone, if the diameter of the cone is 12.4 cm. and the height of the cone is 30 cm.
a.
1206 cm3
b.
1207.4 cm3
c.
1207 cm3
d.
1208 cm3


Solution:

Volume of a cone, V = 13 π r2 h
[Formulae.]

r = 6.2 cm.; h = 30 cm.
[ Radius is half of diameter.]

V = 13 × 3.141 × 6.2 × 6.2 × 30
[Substituting the values.]

= 1207.4 cm.3
[Simplify.]

Therefore, the volume of the cone is 1207.4 cm.3.


Correct answer : (2)
 14.  
Find the volume of the pyramid.

a.
52.26 cm3
b.
52 cm3
c.
53 cm3
d.
51 cm3


Solution:

Volume of the pyramid, V = 13 B h
[Formulae.]

V = 13 × 49 × 3.2
[Here, B = s × s (i.e., area of a square) and substituting the values.]

= 52.26 cm.3
[Simplify.]

So, the volume of the pyramid is 52.26 cm.3.


Correct answer : (1)
 15.  
Find the volume of the figure given.


a.
314 π in3
b.
110 π in3
c.
3.14 π in3
d.
100 π in3


Solution:

Volume of a cone, V= 13 π r2 h
[Formula.]

Here, r = 5 in.; h = 6 + 6 = 12 in.

V = 13 × π × 5 × 5 × 12
[Substituting the values.]

= 100 π in.3
[Simplify.]

The volume of a given figure is 100 π in.3.


Correct answer : (4)
 16.  
Base radius of a cone is 5 in. and its height is 15 in. If the height and the radius of the cone are doubled, then find the volume of the new cone.[Use π = 3.]
a.
1500 in.3
b.
9000 in.3
c.
900 in.3
d.
3000 in.3


Solution:

Base radius of the new cone = 2 × radius of the initial cone = 2 × 5 = 10 in.
[Since base radius of new cone is double the radius of initial cone.]

Height of the new cone = 2 × height of the initial cone = 2 × 15 = 30 in.
[Since height of new cone is double the height of initial cone.]

Volume of cone = 1 / 3πr2h
[Formula.]

= 3000
Volume of new cone = 1 / 3× 3 × 102 × 30
[Substitute the values in the formula and simplify.]

Volume of the new cone is 3000 in.3.


Correct answer : (4)
 17.  
The circumference of the base of a cone of height 15 in. is 44 in. Find the volume of the cone. (Use π = 22 7)
a.
770 in.3
b.
766 in.3
c.
784 in.3
d.
774 in.3


Solution:

Circumference of the base of a cone = 2πr
[Formula.]

r = 44 in.
[Since circumference of a cone is 44 in.]

2 × 227 × r = 44

r = 7 in.
[Simplify.]

Volume of the cone = 1 / 3πr2h
[Formula.]

= 13 × 227 × 72 × 15
[Substitute the values.]

= 770
[Simplify.]

Volume of the cone = 770 in.3.


Correct answer : (1)
 18.  
A bucket is in the shape of a frustum of a cone with a height(x) of 12 cm, diameter of the top portion(a) 48 cm and diameter of bottom portion(b) 16 cm. Find the capacity of the bucket. [Take π = 3.]

a.
29952 cm3
b.
2688 cm3
c.
9984 cm3
d.
2304 cm3


Solution:


The bucket can be considered as a cone with the upper part removed.
[Analysis.]

ΔFBA represents the full cone, ΔEBD represents the part of the cone removed.
[From the figure.]

ΔOAB ~ ΔCDB.
[From the figure.]

OA / CD= OB / BC
[From step 3.]

482162=12+yy
[Substitute.]

y = 16×1248-16 6
[Simplify.]

The volume of the bucket = Volume of the cone with base diameter 48 cm - Volume of the cone with base diameter 16 cm
[Formula.]

Height of cone with diameter 48 cm = 6 + 12 18 cm

Height of cone with diameter 16 cm = 6 cm

Volume of the cone with diameter 48 cm = 1 / 3× 3 × 4824 × 18 10368 cm3
[Volume of the cone = 1 / 3π r2 h.]

Volume of the cone with diameter 16 cm = 1 / 3× 3 × 4824 × 6 = 384 cm3
[Formula.]

Volume of the bucket = 10368 - 384 9984 cm3
[Simplify.]

Capacity of the bucket = 9984 cm3


Correct answer : (3)
 19.  
The circumference of the base of a cone of height 18 in. is 44 in. Find the volume of the cone.
a.
939.18 in.3
b.
924.38 in.3
c.
919.58 in.3
d.
929.18 in.3


Solution:

Circumference of the base of a cone = 2πr
[Formula.]

r = 44 in.
[Since circumference of a cone is 44 in.]

2 × π × r = 44

r = 7.0029 in.
[Simplify.]

Volume of the cone = 1 / 3πr2h
[Formula.]

= 924.38
[Simplify.]

Volume of the cone = 924.38 in.3.


Correct answer : (2)
 20.  
Which of the following statements is true?
a.
The volume of a pyramid is 1 3 times the product of base area and height.
b.
The volume of a prism is 1 3 times the sum of base area and height.
c.
The volume of a pyramid is 1 2 times the product of base area and height.
d.
The volume of a prism is 1 2 times the product of base area and its height.


Solution:

The volume of a pyramid is 1 / 3 times the product of base area and height.

So, the statement, 'The volume of a pyramid is 1 / 3 times the product of base area and height' is true.


Correct answer : (1)

*AP and SAT are registered trademarks of the College Board.