Question

A solid is in the form of a right circular cylinder, with a hemisphere at one end and a cone at the other end. The radius of the common base is 3.5 cm and the heights of the cylindrical and conical portions are 10 cm. and 6 cm, respectively. Find the total surface area of the solid. (Use $(\pi=\frac{22}{7})$)

Answer 1

Answer:

The total surface area of the solid is 373.45 cm²

Step-by-step explanation:

Given :  

Height of the conical part  (h) = 6 cm

Height of the cylindrical part , H = 10 cm

Radius of the cone & cylinder, (r) = 3.5 cm                  

Let, ‘l’ be the slant height of cone.

l = √r² + h²

l = √3.5² + 6² = √12.25 + 36 = √48.25  

l = √48.25

l = 6.95 cm

Slant height of the cone (l) = 6.95 cm

Curved surface area of the cone (S1) = πrl

S1 = 22/7 × (3.5)(6.95) = 22 × 0.5 × 6.95

S1 = 76.45 cm²

Curved surface area of the cylinder  (S2) = 2πrH  

S2 = 2 × 22/7 × 3.5 × 10

= 2 × 22 × 0.5 × 10 = 44 × 5  

S2 = 220 cm²

Curved surface area of the cylinder  (S3) = 2πr²

S3 = 2 × 22/7 × 3.5² = 2 × 22/7 × 3.5 × 3.5

= 2 × 22 × 0.5 × 3.5 = 44 × 1.75 = 77 cm²

S3 = 77 cm²

Total surface area of solid  (S) = S1 + S2 + S3

S = 76.45 + 220 + 77  

S = 373.45 cm²  

Hence, the total surface area of the solid is 373.45 cm² .

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Answer 2

HIII. ....

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