[tex]koi \: bhi \: noi \: h \: kya[/tex]
= 182 x 22/7 = 26 x 22 = 572 cm?
– A toy is in the form of a cone of radius 3.5 cm
mounted on a hemisphere of same radius. The
total height of the toy is 15.5 cm. Find the total
surface area of the toy.
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214.5 cm²
Step-by-step explanation:
Given:
➜ A toy is in the form of a cone of radius 3.5 cm mounted on a hemisphere of same radius. The total height of the toy is 15.5 cm.
Find:
➜ Find the total surface area of the toy.
According to the given question:
➜ 3.5 cm = radius of the cone and the hemisphere.
➜ 15.5 cm = total height of the toy.
➜ 12 cm = height of the cone = (3.5 – 15.5 = 12cm).
Calculations:
➜ Slant height of cone (I) = √h² + r²
➜ I = √12² + (3.5)²
➜ I = √12² + (7/2)²
➜ I = √144 + 49/4 = √(576 + 49)/4 = √625/4
➜ I = 25/2
Formulas:
πrl is curved surface area of cone.
2πr2 is the curved surface area of the hemisphere.
➜ (22/7 × 7/2 × 25/2) = 275/2 cm²
➜ 2 × 22/7 × (7/2)
➜ 2 77 cm²
Formula:
Total surface area of toy = Curved Surface Area of cone + Curved Surface Area of hemisphere.
➜ (275/2 + 77) cm²
➜ (275 + 154)/2 cm²
➜ 429/2 cm²
➜ 214.5 cm²
Therefore, 214.5 cm² is the total surface area of the toy.
Answer:
214.5cm²
Step-by-step explanation:
Total surface area of toy = Curved surface area of cone + surface area of hemisphere
Curved surface area of cone = πrl
=> Where r = 3.5cm,
=> Height = 15.5 − 3.5 = 12cm
And hence, l=12.5cm(by using formula l²=h²+b²)
Therefore C.S.A. of cone = π×3.5×12.5
= 137.5cm²
Surface area of hemisphere =2πr²
=2×π×(3.5)²
=77cm²
Hence T.S.A of toy = 77+137.5
= 214.5cm²