Question

what time is in the form of a cone mounted on a hemisphere of radius 3.5 CM the total height of the tower is 15.5 cm find the total surface area and volume of the toy​

Answer 1

Answer :

1. Total surface area = 214.5 cm³
2. Total volume = 243.8 cm³

Step-by-step solution :

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 = πrl

Curved surface area of cone = 22/7 × 3.5 × l
= 22 × 0.5 × l
= 11 × slant height

Since l = √( r² + h² )
l = √( 3.5² + 12² ) = √156.25
Slant Height = 12.5 cm

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

Now, we know that

Volume of cone = ⅓ πr²h and hemisphere = ⅔πr³

Total volume = ⅓ πr²h + ⅔ πr³
= ⅓πr²( h + 2r )
= 1/3 × 22/7 × 3.5²( 12 + 2 × 3.5 ) cm³
= ⅓ × 22 × 0.5 × 3.5 × 19 cm³
= 243.8 cm³