Math, asked by varisuleepuamma, 1 year ago

From a solid cylinder whose height is 2.4 cm and diameter 1.4 cm, a conical cavity of the same height and same diameter is hollowed out. Find the total surface area of the remaining solid to the nearest cm 2 . Given that, Height (h) of the conical part = Height (h) of the cylindrical part = 2.4 cm Diameter of the cylindrical part = 1.4 cm Therefore, radius (r) of the cylindrical part = 0.7 cm Total surface area of the remaining solid will be = CSA of cylindrical part + CSA of conical part + Area of cylindrical base The total surface area of the remaining solid to the nearest cm 2 is 18 cm 2 . Why C.S.A. of cone is added instead of subtracting(cause we have to find T.S.A. of remaining part)??? plz explain

Answers

Answered by shubhamjoshi033
397

Answer:

The total surface area of the remaining solid will be 18 cm²

Step-by-step explanation:

The outer surface area of the cylinder = 2πrh

= 2 x 3.14 x 0.7 x 2.4

= 10.55 cm²

slant height of the cone, L = √(h² + r²)

=√(2.4² + 0.7²)

= √6.25

= 2.5 cm

hence outer surface area of the cone = πrL

= 3.14 x 0.7 x 2.5

= 5.5 cm²

This outer surface area of the cone is equal to the inner surface area of the hollow portion of the cylinder left.

surface area of the cylindrical base = πr²

= 3.14 x 0.7²

= 1.54 cm²

Hence total surface area of the remaining solid = The outer surface area of the cylinder + inner surface area of the hollow portion of the cylinder left + surface area of the cylindrical base

= 10.55 + 5.5 + 1.54

= 17.59 cm²

= 18 cm² (rounded off to nearest cm²)

Hence the total surface area of the remaining solid will be 18 cm²

Answered by angelsara497
214

Answer:

Step-by-step explanation:

Height of cylinder = Height of conical cavity, h = 2.4 cm

Diameter, d = 1.4 cm

Radius, r = 1.4/2= 0.7 cm

Slant height, l = √h² + r² = √(2.4)² + (0.7)² = √5.76 + 0.49 = √6.25 = 2.5 cm

TSA of the remaining solid = CSA of cylindrical part + CSA of conical part + Area of cylindrical base

TSA = 2πrh+ πrl+ πr²

= πr [ 2(h) + l + r ]

= 22/7 × 0.7 [ 2 × 2.4 + 2.5 + 0.7 ]

= 17.6 cm²

Hence,

TSA of remaining solid is = 17.6

Hope it helps you

Cheers!!

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