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 of cone = 3.5 cm
• Height of toy = 15.5 cm

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To find:

• Total surface area of toy.

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SoluTion:

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☯ Toy is hemispherical at bottom and conical at top.

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Therefore,

T.S.A of toy = C.S.A of hemisphere + C.S.A of cone

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Slant height of cone, l = $\sf \sqrt{h^2 + r^2}$

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$:\implies\sf l = \sqrt{3.5^2 + 12^2}$

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$:\implies\sf l = \sqrt{12.25 + 144}$

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$:\implies\sf l = \sqrt{156.25}$

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$:\implies{\underline{\boxed{\sf{\pink{l = 12.5\;cm}}}}}\;\bigstar$

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Therefore,

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$\;\;\;\;\;\;\;\;\star\;\sf 2 \pi r^2 + \pi rl$

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$:\implies\sf 2 \pi (3.5)^2 + \pi (3.5)(12.5)$

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$:\implies\sf 24.5 \pi + 43.75 \pi$

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$:\implies\sf 68.25 \pi$

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$:\implies\sf 68.25 \times \dfrac{22}{7}$

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$:\implies{\underline{\boxed{\sf{\purple{214.5\;cm^2}}}}}\;\bigstar$

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$\therefore$ Hence, Total surface area of toy is 214.5 cm².

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Related formulas:

• TSA of Sphere = 4πr²

• Volume of sphere = $\sf \dfrac{4}{3} \pi r^3$

• TSA of hemisphere = 3πr²

• CSA of hemisphere = 2πr²

• Volume of hemisphere = $\sf \dfrac{2}{3} \pi r^3$

• TSA of cone = πr(r + l)

• CSA of cone = πrl

• TSA of cylinder = 2πr(r + h)

• CSA of cylinder = 2πrh

• TSA of cylinder = πr²h

Answer 2

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Answer:

We have,

• Radius of cone = Radius of hemisphere = 3.5 cm.

• Height of the toy = 15.5 cm

To calculate the CSA of cone we have to find first the Slant Height of the cone :]

Slant Height (l)² = h² + r²

Slant Height = (15.5)² + (3.5)²

Slant Height = 12.25 + 144

Slant Height (l) = 156.25 cm²

Slant Height = 12.5 cm

Now, we will calculate the TSA of the toy :

➳ TSA of toy = CSA of hemisphere + CSA of cone

➳ TSA of toy = 2πr² + πrl

➳ TSA of toy = 2π(3.5)² + π(3.5)(12.5)

➳ TSA of toy = 24.5π + 43.75π

➳ TSA of toy = 68.25π

➳ TSA of toy = 68.25 * 22/7

➳ TSA of toy = 214.5 cm²

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$\boxed{\underline{\underline{\bigstar \: \bf\:Extra\:Brainly\:knowlegde\:\bigstar}}}$

$\boxed{\bigstar{\sf \ Cylinder :- }}\\ \\\sf {\textcircled{\footnotesize1}} Volume \ of \ Cylinder= \pi r^2 h \\ \\ \\ \sf {\textcircled{\footnotesize2}}\ Curved \ surface\ Area \ of \ cylinder= 2\pi r h\\ \\ \\ \sf {\textcircled{\footnotesize3}} Total \ surface \ Area \ of \ cylinder= 2\pi r (h+r)$

$\boxed{\bigstar{\sf \ Cone :- }}\\ \\\sf {\textcircled{\footnotesize1}} Volume \ of \ Cone= \dfrac{1}{3}\pi r^2 h \\ \\ \\ \sf {\textcircled{\footnotesize2}}\ Curved \ surface\ Area \ of \ Cone = \pi r l \\ \\ \\ \sf {\textcircled{\footnotesize3}} Total \ surface \ Area \ of \ Cone = \pi r (l+r) \\ \\ \\ \sf {\textcircled{\footnotesize4}} Slant \ Height \ of \ cone (l)= \sqrt{r^2+h^2}$

$\boxed{\bigstar{\sf \ Hemisphere :- }}\\ \\\sf {\textcircled{\footnotesize1}} Volume \ of \ Hemisphere= \dfrac{2}{3}\pi r^3 \\ \\ \\ \sf {\textcircled{\footnotesize2}}\ Curved \ surface\ Area \ of \ Hemisphere = 2 \pi r^2 \\ \\ \\ \sf {\textcircled{\footnotesize3}} Total \ surface \ Area \ of \ Hemisphere = 3 \pi r^2$

$\boxed{\bigstar{\sf \ Sphere :- }}\\ \\\sf {\textcircled{\footnotesize1}} Volume \ of \ Sphere= \dfrac{4}{3}\pi r^3 \\ \\ \\ \sf {\textcircled{\footnotesize2}}\ Surface\ Area \ of \ Sphere = 4 \pi r^2$