Surface Areas and Volumes MCQs

Ans: d) 1568 m³, 868 cm²

Explanation: Given: l = 16 m, b = 14 m, h = 7 m.

As we know, Volume = l*b*h                           

= 16*14*7                       

= 1568 m³

Also, Surface area = 2(lb+bh+lh)                        

= 2(16*14 + 14 * 7 + 16*7)                      

= 2* 234          

= 868 cm²

Ans: b) 12 cm

Explanation: As we know, Slant height ( l ) = √h²+r² units.

Here, r = 5 cm and l = 13 cm, h =?

So, the formula to find height (h) is, h = √l²- r²                                                      

= √(13)²- (5)²                                          

= √169 - 25 = √144                                             

= 12 cm

So, the height is 12 cm.

Ans: a) 15 m

Explanation: Given, Dimension of the room is, l = 10m, b = 10 m, h = 5m

Therefore, length of the longest pole = Diagonal of a cuboid i.e., room

And Diagonal is given by the formula, 

√l²+b²+h²                                                 

= √(10)²+(10)²+(5)²                                                    

= √100+100+25                                              

= √225                                               

= 15 m.

So, the length of the longest pole that can be placed in a room of dimensions (10 m × 10 m × 5 m) is 15m.

Ans: b) 164.85 sq.cm

Explanation: Given, the base diameter of a cone (d) = 10.5 cm, then radius of the cone (r) = d/2

                         R = 10.5 /2 

                         r = 5.25

Also, slant height of the cone (l) = 10 cm

Then, the curved surface area is given by formula, 

πrl                                                                

= 3.14*5.25*10                                                          

= 16.485*10                                            

= 164.85 sq.cm

So, the curved surface area of the cone is 164.85 sq. cm.       

Ans: 2.1 cm    

Explanation:  Given, the height of the cone = 8.4 cm, a radius of its base = 2.1 cm, the radius of the sphere =?

The formula to find the volume of the cone is 1/ 3 πr²h    

So, by putting the values in the given formula we get, (1/3)π(2.1)² (8.4)  

The volume of the cone = (1/3)π(2.1)² (8.4)  ------------------------(1)  

Now, the volume of the sphere = 4/3 πR³

4/3 πR³ = (1/3)π(2.1)² (8.4)                            

4R³ = (2.1)² (8.4)

R³ = ((2.1)²(8.4) ) / 4

R³ = (2.1)² (2.1)

R³ = (2.1)³

R = 2.1 cm

So, the radius of the sphere is 2.1 cm.

Ans: c) 5544 sq.cm

Explanation: Given, radius of the sphere(r) = 21 cm.

The surface area of sphere = 4πr²

                                        = 4 * 22/7 * 21* 21

                                       = 4* 22* 3 * 21

                                      = 5544 cm²

So, the surface area of a sphere of radius 21 cm is 5544 sq. cm.

Ans: b) 20: 27

Explanation: Let the radii of the cylinders be R1 and R2 and their heights are H1 and H2.

Therefore, the ratio of the radius = R1/R2 = â??

Similarly, the ratio of the height = H1/H2 = 5/3

To find, the ratio of the volumes of the cylinders = V1/V2 =?

Let us assume, V1 = Volume of the first cylinder = πR1²H1

Similarly, V2 = Volume of the second cylinder = πR2²H2

V1/V2 = πR1²H1 / πR2²H2 

               = R1²H1 / R2²H2

              = (R1/R2)² * (H1/H2)

              = 4/9 * 5/3

             = 20/27

V1/V2 = 20: 27

So, the ratio of the volumes of the cylinders is 20:27

Ans: d) 216 sq.cm

Explanation: Given edge of the cube (a) = 6cm

The formula of the surface area of a cube = 6a²                                       

= 6 * (6)²                                                      

= 6 * 36                                                                    

= 216 sq.cm.

So, the surface area of a cube with a 6 cm edge is 216 sq. cm.

Ans: c) 1 cm      

Explanation:  Given, curved surface area of the cylinder (a) = 4.4 sq.cm, radius of the cylinder(r) = 0.7 cm. To find, height of the cylinder(h) =?

As we know, the curved surface area of the cylinder = 2πrh                                                    

4.4 = 2 * (22/7) * 0.7 * h                                        

4.4 = 2 * 22* 0.1 * h                                        

4.4 / (2 * 22* 0.1) = h                  

4.4 / 4.4 = h                                                  

1 = h

Therefore, h = 1 cm.

The height of the cylinder is 1 cm.

Ans: (b) 36 kg

The shape of the beam is cuboid. So, the volume of a cuboid is given by, l*b*h

Given: l = 9 m, 

b = 40 cm = 40 / 100 m = 0.4 m

h = 20 cm = 20 / 100 m = 0.2 m

So, putting the values in the formula we get,

l*b*h = 9*0.4*0.2 = 0.72 m

So, the volume of the beam is 0.72 m

Now, if the iron weighs 50 kg per cubic meter, the weight of the beam = 0.72 * 50 = 36 kg

Therefore, the weight of the beam = 36 kg.

Ans: a) 1 

Explanation: The box has the shape of a cuboid. So, the volume of a cuboid is given by, l*b*h.

Now, we have, l = 5m, b = 2m, h = 10 cm = 10/ 100 = 0.1 m

So, the volume of the sand that can be filled in the rectangular box = 5*2*0.1 = 10*0.1 = 1 m³.

Ans: (c) same

Explanation: Determine the Curved Surface Area of a Cylinder using the given conditions.

Assume r is the radius of the cylinder and h is the height of the cylinder.

The cylinder's curved surface area is 2πrh.

If the radius is doubled and the height is cut in half,

R=2r, H = h/2

The cylinder's curved surface area =2πRH

= 2(2r) π (h/2)

= 2πrh

As a result, the cylinder's curved surface area will be the same.