a toy is in the form of a cone mounted on a hemisphere of radius 3.5 cm. the total height of the toy is 15.5 cm . find the total surface area and volume of the toy
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Answered by
9
Answer:
214.5
Step-by-step explanation:
csa of hemisphere = 2πr^2
= 2*22/7*3.5*3.5
=2*22*0.5*3.5
= 77 cm^2
csa of cone = πrl
l = √ r^2 +h^2
= √(3.5)^2 + (12)^2
=√12.25+144
= 12.5
csa of cone= 22/7*3.5*12.5
= 137.5
tsa of toy = 214.5
Answered by
9
:
1. Total surface area = 214.5 cm³
2. Total volume = 243.8 cm³
In a hemisphere, its height and radius are equal.
So if total height of toy is 15.5 cm then height of only cone = 15.5 cm - 3.5 cm = 12 cm
Curved surface area of cone = 22/7 × 3.5 × l
= 22 × 0.5 × l
= 11 × slant height
l = √( 3.5² + 12² ) = √156.25
So, C.S.A of cone = 11 cm × 12.5 cm
= 137.5 cm²
Curved surface area of hemisphere = 2πr²
= 2 × 22/7 × 3.5 × 3.5 cm²
= 2 × 22 × 0.5 × 0.5 cm²
= 77 cm²
Total Surface area = 77 + 137.5 cm²
= 214.5 cm²
Volume of cone = ⅓ πr²h and
hemisphere = ⅔πr³
= ⅓πr²( h + 2r )
= 1/3 × 22/7 × 3.5²( 12 + 2 × 3.5 ) cm³
= ⅓ × 22 × 0.5 × 3.5 × 19 cm³
=
1. Total surface area = 214.5 cm³
2. Total volume = 243.8 cm³
In a hemisphere, its height and radius are equal.
So if total height of toy is 15.5 cm then height of only cone = 15.5 cm - 3.5 cm = 12 cm
Curved surface area of cone = 22/7 × 3.5 × l
= 22 × 0.5 × l
= 11 × slant height
l = √( 3.5² + 12² ) = √156.25
So, C.S.A of cone = 11 cm × 12.5 cm
= 137.5 cm²
Curved surface area of hemisphere = 2πr²
= 2 × 22/7 × 3.5 × 3.5 cm²
= 2 × 22 × 0.5 × 0.5 cm²
= 77 cm²
Total Surface area = 77 + 137.5 cm²
= 214.5 cm²
Volume of cone = ⅓ πr²h and
hemisphere = ⅔πr³
= ⅓πr²( h + 2r )
= 1/3 × 22/7 × 3.5²( 12 + 2 × 3.5 ) cm³
= ⅓ × 22 × 0.5 × 3.5 × 19 cm³
=
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