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Asked/Added Questions From NCERT:


Question 1. Asked on :19 January 2019:10:07:46 AM

 Three spheres having radii 2 cm ,3 cm and 5 cm are melted together to from a single find the radius of the new sphere.

-Added by Prince Rawat Mathematics » SURFACE AREAS AND VOLUMES

Answer:

Himanshi Verma

 Let three spheres are S1, S2 & S3

having radii r₁ = 3cm, r₂ = 4cm & r₃ = 5cm respectively.

Let the radius of new Big sphere S is R.

A/Q,

Volume of new Sphere  S = Sum of volumes three Spheres S1, S2 & S3

⇒ 4/3πR³ = 4/3π(r₁)³ + 4/3π(r₂)³+4/3π(r₃)³

⇒ 4/3πR³ = 4(r₁³ +r₂³ + r₃³)/3π

⇒ R³ = r₁³ +r₂³ + r₃³

⇒  R³ = 3³ +4³ + 5³ = 27 + 64 + 125

⇒ R³ =  216

⇒ R = ∛216

⇒ R = 6cm

Therefore radius of new Sphere is 6 cm.

-Answered by Himanshi Verma On 20 January 2019:05:15:36 PM


Question 2. Asked on :19 January 2019:10:05:05 AM

 The slant height of a cone is 10 cm and its base radius is 8 cm find total surface area of the cone.

-Added by Prince Rawat Mathematics » SURFACE AREAS AND VOLUMES

Answer:

Himanshi Verma

  slant height of cone is : 10 

Radius of the base is : 8 cm

Total surface area of cone is : πr(l+r)

227 ×8(10+8) 

227 ×144

= 452.57

-Answered by Himanshi Verma On 20 January 2019:04:27:57 PM


Question 3. Asked on :15 January 2019:09:48:55 AM

 The lateral surface area of a cube is 256cm2. Find its volume.

-Added by Prince Rawat Mathematics » SURFACE AREAS AND VOLUMES

Answer:

Himanshi Verma

  Lateral Surface Area of cube=256 cm²

4(side)² =256
side²=256÷4
side²=64
side=√64=8 cm
Volume of the cube=(side)³=8×8×8=512 cm³.

-Answered by Himanshi Verma On 16 January 2019:06:04:58 PM


Answer:

Himanshi Verma

 l=5m    b=4m      h=3m 

The total area of cuboid = 2(lb+bh+hl)+l×b

                                  = 2(5×4+4×3+3×5)+5×4

                                  = 2(20+12+15)+20

                                  = 2(47) +20

                                  =    94+20

                                  =     114m2

The cost of white washing the wall and the ceiling of the room = 7.50 per m2

      The cost of 114m2 of the walls and ceiling of the room= (7.50×114)Rs

                                                                                   = 855.00Rs.

                                                                            

-Answered by Himanshi Verma On 19 January 2019:05:10:07 PM


Question 5. Asked on :15 January 2019:09:27:40 AM

 Find the ratio of total surface area of sphere and a hemisphere of same radius.

-Added by Prince Rawat Mathematics » SURFACE AREAS AND VOLUMES

Answer:

Himanshi Verma
The total surface area of sphere= 4πr2

The total surface area of hemisphere= 3πr2

The ratio of total surface area of sphere and hemisphere= 4πr2/3πr2

                                                                                = 4:3

-Answered by Himanshi Verma On 20 January 2019:04:38:18 PM


Question 6. Asked on :15 January 2019:09:24:30 AM

 The total surface area of a cube is 150sq. cm. Find the perimeter of  any one of its faces. 

-Added by Prince Rawat Mathematics » SURFACE AREAS AND VOLUMES

Answer:

Himanshi Verma

   Total surface area of cube is 150sq. cm

Total surface area of cube : 6a2

To find perimeter of its one faces :  ?

Total surface area of cube =150sq.cm

                           6a2  =150sq.cm

 = 1506 

= 25cm

=a2 = √25cm

=a = 5 cm

Perimeter of its one face is = 4 × a

                                        = 4 × 5 cm

                                        = 20 cm Answer

-Answered by Himanshi Verma On 19 January 2019:04:39:34 PM


Question 7. Asked on :15 January 2019:09:20:19 AM

 The surface area of the cuboid is 1372 sq. cm. If its dimensions are in the ratio of 4:2:1. Then find length. 

-Added by Prince Rawat Mathematics » SURFACE AREAS AND VOLUMES

Answer:

Himanshi Verma

 The surface area of the cuboid= 1372 sq. cm 

  Let the dimensions =4x, 2x, 1x

     The total surface area of the cuboid = 2(lb+bh+hl)=1372

                                                        = 2(4x × 2x + 2x × 1x + 4x × 1x )=1372 

=2(8x2+2x2+4x2) =1372

=2(14x2)= 1372

=28x2=1372

= x2=1372/28

       = 49

x=7m

the dimensions are 4x=4×7=28m

                           2x=2×7=14m

                           1x=1×7=7m

 

  

-Answered by Himanshi Verma On 19 January 2019:05:17:58 PM


Question 8. Asked on :14 January 2019:10:35:56 AM

 The ratio of height of two cylinder is 5:3 as well as the ratio of their radii is 2:3. find the ratio of the volume of the cylinder. 

-Added by Prince Rawat Mathematics » SURFACE AREAS AND VOLUMES

Answer:

Himanshi Verma

 Let the radii be 2x and 3x,

let the height be 5y and 3y.

so, ratio of volume =r²h/R²H =(2x)²×5y/(3x)²×3y =20x²y/27x²y =20/27,

The ratio is = 20:27

-Answered by Himanshi Verma On 20 January 2019:05:11:58 PM


Question 9. Asked on :11 January 2019:10:10:33 AM

 The volume of sphere is 310.4 cm3. Find its radius.

-Added by Prince Rawat Mathematics » SURFACE AREAS AND VOLUMES

Answer:

Himanshi Verma

 

volume of the sphere = 43 πr3= 310.4cm3

                                4/3×22/7×r3=310.4

                                88/21×r3= 310.4

                                   r3=   310.4×21/88

                                      =   6518.4/88

                                   r3  = 74.0727272cm

-Answered by Himanshi Verma On 19 January 2019:04:56:34 PM


 

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