# VOLUME OF 3D SHAPES QUESTIONS WITH ANSWERS

Volume of 3D Shapes Questions with Answers :

Here we are going to see, some practice questions on volume of 3D shapes.

## Volume Formulas for 3D Shapes

 Volume  =  Πr2h Volume  =  Πh(R2 - r2) Volume  =  (1/3) Πr2h Volume  =  (4/3) Πr3Volume of hollow sphere  =  (4/3) Π(R3 - r3) Volume  =  (2/3) Πr3 Volume = (2/3)Π(R3 - r3) Volume = (1/3)Πh(R2 + r2 + Rr)

## Volume of 3D Shapes Questions with Answers

To find questions from 1 to 3, please visit the page "VOLUME OF 3D SHAPES EXAMPLES".

Question 5 :

A right angled triangle whose sides are 6 cm, 8 cm and 10 cm is revolved about the sides containing the right angle in two ways. Find the difference in volumes of the two solids so formed.

Solution :

The longest side of a triangle is 10 cm

If the triangle is revolved about 6 cm

r = 6 cm and h = 8 cm

Volume of solid, when it is revolved about 6 cm,

=  (1/3)πr2h

=  (1/3)π 6(8)

=  96π cm3

Volume of solid, when it is revolved about 8 cm,

r = 8 cm and h = 6 cm

=  (1/3)πr2h

=  π 8(6)

=  128π cm3

Difference  =  128π - 96π

=  32π cm3

=  32(22/7)

=  100.5 cm3

Now let us see the solution of the next problem on "Volume of 3D Shapes Questions with Answers".

Question 6 :

The volumes of two cones of same base radius are 3600 cm3 and 5040 cm3. Find the ratio of heights.

Solution :

Let "h1" and "h2" be the heights of 1st and 2nd cone.

Volume of 1st cone  =  3600 cm3

(1/3)πr2h1  =  3600 cm3

Volume of 2nd cone  =  5040 cm3

(1/3)πr2h2  =  5040 cm3

h1 : h2  =  3600 : 5040

h1 / h2  =  3600 / 5040

h1 : h2  =  5 : 7

Now let us see the solution of the next problem on "Volume of 3D Shapes Questions with Answers".

Question 7 :

If the ratio of radii of two spheres is 4 : 7, find the ratio of their volumes.

Solution :

Radius of 1st sphere (r1) =  4x

Radius of 2nd sphere  (r2)  =  7x

Volume of sphere  =  (4/3) πr3

(4/3) πr13 (4/3) πr13

(4x)3 : (7x)3

64 : 343

Question 8:

A solid sphere and a solid hemisphere have equal total surface area. Prove that the ratio of their volume is 3 : 4 .

Solution :

Total surface area of sphere = 4πr12

Total surface area of hemisphere = 3πr22

4πr12= 3πr22

r12= (3/4)r22

r1  = (√3/2)r2

Volume of sphere  =  (4/3) πr13

Volume of hemisphere  =  (2/3) πr13

(4/3) πr13 : (2/3) πr23

2((√3/2))3 : r23

2(3√3/8)  r23r23

3√3 : 4

Hence it is proved.

Question 9 :

The outer and the inner surface areas of a spherical copper shell are 576π cm2 and 324π cm2 respectively. Find the volume of the material required to make the shell.

Solution :

Outer curved surface area of sphere  =  4πR2

Inner curved surface area of sphere  =  4πr2

4πR=  576π

R2  =  576/4  =  144

R  =  12

4πr2  =  324π

r2  =  324/4  =  81

r  =  9

Volume of sphere  =  (4/3) π (R3r3)

=  (4/3) π (123 - 93)

=  (4/3) π (1728 - 729)

=  (4/3) π (999)

=  1332(22/7)

=  4186.28 cm3

Question 10 :

A container open at the top is in the form of a frustum of a cone of height 16 cm with radii of its lower and upper ends are 8 cm and 20 cm respectively. Find the cost of milk which can completely fill a container at the rate of 40 per litre.

Solution :

Volume of milk in the frustum container

= (1/3)Πh(R+ r2 + Rr)

h = 16 cm, r = 8 cm, R = 20 cm

= (1/3)Π (16)(20+ 82 + 20(8)) - Πr2

=  (22/7) [(1/3)(16)(20+ 82 + 20(8)) - 64]

=  (22/7) [(1/3)(16)(624) - 64]

=  (22/7) [3264]

=  10258.28 cm3

1000 cm3  =  1 liter

=  10.25828 liter

Cost per liter  =  40

=  40(10.258)

=  410.32

After having gone through the stuff given above, we hope that the students would have understood, "Volume of 3D Shapes Questions with Answers".

Apart from the stuff given in this section "Volume of 3D Shapes Questions with Answers" if you need any other stuff in math, please use our google custom search here.