A toy is in the form of cone mounted on a hemisphere of diameter 7cm. the total height of the toy is 14.5cm. find the volume and total surface area of the toy
Answers
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Answer:
Step-by-step explanation:
Solution :-
Diameter of hemisphere = 7 cm
Radius of hemisphere, r = 7/2 = 3.5 cm
Height of hemisphere = 14.5 cm
Height of cone = 14.5 - 3.5 = 11 cm
Height of hemisphere = 3.5 cm
To Find :-
Volume of toy
Total surface area of the toy
Formula to be used :-
Volume of toy (cone + hemisphere) = 1/3 × π × r² [h + 2π]
Total surface area of toy (cone + hemisphere) = πr[l + 2r]
Solution :-
Volume of toy = 1/3 × π × r² [h + 2π]
⇒ Volume of toy = 1/3 × 22/7 × 3.5 × 3.5 × [11 + 2 × 3.5]
⇒ Volume of toy = 1/3 × 22/7 × 12.25 × 18
⇒ Volume of toy = 231 cm³
Now, TSA but we have to find slant height,
Slant height, l = √r² + h²
⇒ l = √(3.5)² + (11)²
⇒ l = √133.22
⇒ l = 11.5
Now, TSA of toy
Total surface area of toy = πr[l + 2r]
⇒ Total surface area of toy = 22/7 × 3.5 × (11.5 + 2 × 3.5)
⇒ Total surface area of toy = 22/7 × 3.5 × 18.5
⇒ Total surface area of toy = 203.5 cm²
Hence, the volume and total surface area of the toy is 231 cm³ and 203.5 cm².