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

✒ Given :-

• Radius = 3.5cm
• Total height of toy = 15.5cm

✒ To Find :-

• Total surface area of the toy.

✒ Solution :-

Radius of hemisphere = 3.5cm

Height of hemisphere = 3.5cm

Radius of cone = 3.4cm

Height of cone = Total height - Height of hemisphere

= 15.5 - 3.5

= 12cm

Curved surface area of Hemisphere = 2πr²

= $2\times\frac{22}{7}\times3.5\times3.5$

= 77cm²

Now, For curved surface area of cone we need to find 'l' i.e., Slant height.

Slant height = $\sqrt{r²+h²}$

= $\sqrt{(3.5)²+(12)²}$

= $\sqrt{12.25+144}$

= $\sqrt{156.25}$

= 12.5cm

Curved surface area of cone = πrl

= $\frac{22}{7}\times3.5\times12.5$

= $\frac{22}{\cancel{7}}\times{\cancel{3.5}}\times12.5$

= $22\times0.5\times12.5$

= 137.5 cm²

Total surface area of toy :-

= curved surface area of hemisphere + curved surface area of cone

= 77cm² + 137.5cm²

$\large{\purple{\underbrace{\red{\boxed{\color{lime}{214.5cm²}}}}}}$

Answer 2

Answer:

✒ Given :-

Radius = 3.5cm

Total height of toy = 15.5cm

✒ To Find :-

Total surface area of the toy.

✒ Solution :-

Radius of hemisphere = 3.5cm

Height of hemisphere = 3.5cm

Radius of cone = 3.4cm

Step-by-step explanation:

Height of cone = Total height - Height of hemisphere

= 15.5 - 3.5

= 12cm

Curved surface area of Hemisphere = 2πr²

2\times\frac{22}{7}\times3.5\times3.5

= 77cm²

Now, For curved surface area of cone we need to find 'l' i.e., Slant height.

Slant height =

\sqrt{(3.5)²+(12)²}\sqrt{(3.5)²+(12)²}

\sqrt{12.25+144}

\sqrt{156.25}

= 12.5cm

Curved surface area of cone = πrl

\frac{22}{7}\times3.5\times12.5

\frac{22}{\cancel{7}}\times{\cancel{3.5}}\times12.5

22\times0.5\times12.5

= 137.5 cm²

Total surface area of toy :-

= curved surface area of hemisphere + curved surface area of cone

= 77cm² + 137.5cm²