Question

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.

Answer 1

Answer:

Step-by-step explanation:

rad.of cone =rad.of hemisphere=3.5 cm (given)

Also,

ht of toy=15.5 cm (given)

ht of hemisphere=3.5 cm

ht of cone=15.5-3.5

=12cm

slant ht. of cone=under root h^2+r^2

=under root (12^2+3.5^2)

=under root 144+12.25

=under root 156.25

= 12.5 cm

CSA of hemisphere = πr²

=> 2×22/7×(3.5)^2

=77 cm^2

CSA of cone = πrl

=> 22/7×3.5×12.5

=137.5 cm^2

TSA of toy=CSA of hemisphere+CSA of cone

=77+137.5

=214.5cm^2

Answer 2

$<b>Answer</b>$ :

1. Total surface area = 214.5 cm³

2. Total volume = 243.8 cm³

$<b>Step-by-step solution :</b>$

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

$<b>Curved surface area of cone = πrl</b>$

Curved surface area of cone = 22/7 × 3.5 × l

= 22 × 0.5 × l

= 11 × slant height

$<b>Since l = √( r² + h² )</b>$

l = √( 3.5² + 12² ) = √156.25

$\sf{\boxed{Slant\: Height \:= \:12.5 \:cm}}$

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

$<b>Now, we know that</b>$

Volume of cone = ⅓ πr²h and

hemisphere = ⅔πr³

$<b>Total volume = ⅓ πr²h + ⅔ πr³</b>$

= ⅓πr²( h + 2r )

= 1/3 × 22/7 × 3.5²( 12 + 2 × 3.5 ) cm³

= ⅓ × 22 × 0.5 × 3.5 × 19 cm³

= $\sf\:243.8 \:cm^3$

$\textbf{please mark as brainliest}$