Question

a solid cylinder is of height 15 cm and diameter 7 cm. two equal conical holes of radius 3 cm and height 4 cm are cut off, one from each circular end. find the surface are of remaining solid.
I WILL MARK CORRECT ANSWER AND EXPLANATION AS BRAINLIEST

Answer 1

hello ...................................

r₁=7/2cm
r₂=3cm
h₁=15cm
h₂=4cm

slant height of cone
l=√r₂²+h₂²
l=√3²+4²
l=√9+16
l=5cm

surface are of remaining solid =C.S.A of cylinder+C.S.A of 2 cones cutted from each end

=2πr₁h₁+2[πr₂l]
=2π[r₁h₁+r₂l]
=2×22/7[7/2×15+3×5]
=44/7[105/2+15]
=44/7[52.5+15]
=44/7×67.5
=44×9.64
=424.16cm²

so surface area of remaining solid is 424.16 cm²

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hope this would help you
@Rohit

Answer 2

Given Diameter of cylinder = 7 cm So
Radius of solid cylinder = 3.5 cm
Height of cylinder = 15 cm

And
Radius of cone = 3 cm
Height of cone = 4 cm 
So ,

Surface area of remaining solid cylinder = Total surface area of cylinder - Area of base of cones + curved surface area of cones

We know
Total surface area of cylinder = 2πr ( r + h ) , So

Total surface area of this solid cylinder = 2× 227 × 3.5 ( 3.5 + 15) ( As we know π = 227 )

Total surface area of this solid cylinder = 22 × 18.5 = 407 cm2

And

Area of base of cone = πr2 , So
Area of base of both cones = 2×πr2

Area of base of both cones = 2×227 × 3 × 3

Area of base of both cones = 3967 = 56.57 cm2

And

Slant height of cone l = h2 + r2−−−−−−−√ = 42 + 32−−−−−−−√ = 16 + 9−−−−−−√ = 25−−√ = 5 cm
we know curved surface area of cone = πrl , So

Curved surface area of both cones = 2 × πrl 

Curved surface area of both cones = 2 × 227 × 3 × 5 

Curved surface area of both cones = 6607 = 94.28 cm2

Then

Surface area of remaining solid cylinder = 407 cm2 - 56.57 cm2 + 94.28 cm2 = 444.71 cm2