a toy is in the shape of a smaller solid hemisphere
mounted on a bigger solid hemisphere. Radius of bigger hemisphere
is 2 cm and that of the smaller is 1 cm. Find the total surface area of
the toy.
Answers
≡QUESTION≡
A toy is in the shape of a smaller solid hemisphere mounted on a bigger solid hemisphere. Radius of bigger hemisphere is 2 cm and that of the smaller is 1 cm. Find the total surface area of the toy.
║⊕ANSWER⊕║
SOMETHING YOU SHOULD KNOW FIRST
Total surface are of hemisphere = 3πr²
Curved surface are of hemisphere = 2πr²
SOLUTION
Let r₁ and r₂ be the radius of large and smaller hemisphere.
Surface area of toy
= {Total surface area of large hemisphere} + {curved surface area of small hemisphere} - {base area of small hemisphere}
Base area of small hemisphere = πr₂²
Surface area of toy = 3πr₁² + 2πr₂² - πr₂²
Surface area of toy = 3πr₁² + πr₂²
= 3π2² + π1²
= 3π*4 + π*1
= 12π + π
= 13π
= 40.82 cm²
Answer:
TSA of Toy = 40.82 cm²
Step-by-step explanation:
We Have :-
A toy
A smalll hemisphere with radius = 1 cm
A bigger hemisphere with radius = 2 cm
To Find :-
TSA of the Toy
Formula Used :-
CSA of Hemisphere = 2 π r²
Area of Circle = π r²
Solution :-
TSA of Toy = CSA of Bigger Hemisphere + CSA of Smaller Hemisphere + Base of Bigger Hemisphere - Base of Smaller Hemipshere
CSA of Bigger Hemisphere = 2 π r²
= 2 * 3.14 * 2 * 2
= 25.12 cm²
CSA of Smaller Hemisphere = 2 π r²
= 2 * 3.14 * 1 * 1
= 6.28 cm²
Base of Bigger Hemisphere = π r²
= 3.14 * 2 * 2
= 12.56 cm²
Base of Smaller Hemisphere = π r²
= 3.14 * 1 * 1
= 3.14 cm²
TSA of Toy = 25.12 + 6.28 + 12.56 - 3.14
= 40.82 cm²