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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

Master Purushottam

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 Master Purushottam On 24 August 2019:12:18:19 AM

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

Master Purushottam

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 Master Purushottam On 24 August 2019:12:15:34 AM

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

Master Purushottam

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 Master Purushottam On 24 August 2019:12:03:45 AM

Master Purushottam

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 Master Purushottam On 24 August 2019:12:04:01 AM

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

Master Purushottam
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 Master Purushottam On 24 August 2019:12:04:08 AM

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

Master Purushottam

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

-Answered by Master Purushottam On 24 August 2019:12:01:30 AM

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

Master Purushottam

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 Master Purushottam On 24 August 2019:12:01:38 AM

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

Master Purushottam

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 Master Purushottam On 23 August 2019:11:57:01 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

Shivang Gupta

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 Shivang Gupta On 25 August 2019:03:29:31 PM

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