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 a toy is 15.5 cm find the total surface area of a toy​

Answer 1

Step-by-step explanation:

The total surface area of the conical toy of radius 3.5 cm mounted on a hemisphere of the same radius if the total height of the toy is 15.5 cm is 214.5 cm2.

Answer 2

☘️ Given:

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

☘️ To find:

• The total surface area of the toy.

☘️ Solution:

So,

→ T.S.A (Total surface area) of toy = C.S.A(curved surface area) of cone + C.S.A of hemisphere

→ T.S.A (Total surface area) of toy = πrl + 2πr²

As we can see, we first need to find the slant height (l):

$\sf→ \: l \: = \sqrt{(r) {}^{2} + (h) {}^{2} }$

Height of cone (h) = total height of cone - height of hemisphere

h = 15.5 - 3.5

h = 12 cm

So,

$\sf→ \: l \: = \sqrt{( {3.5)}^{2} + ( {12)}^{2} } \\ \sf→ \: l \: = \sqrt{12.25 + 144} \\ \sf→ \: l \: = \sqrt{156.25} \\ \sf→ \: l \: =12.5$

Now, let's put the value of slant height (l) in formula:

→ T.S.A of toy = πrl + 2πr²

→ T.S.A of toy = πr(l + 2r)

→ T.S.A of toy = 22/7 × 3.5(12.5 + 2×3.5)

→ T.S.A of toy = 22/7 × 3.5(12.5 + 7)

→ T.S.A of toy = 22 × 0.5(19.5)

→ T.S.A of toy = 110(19.5)

→ T.S.A of toy = 214.5 cm²

So, the total surface area of the toy = 214.5 cm².

☘️ Answer:

• 214.5 cm² is the answer.