# a toy is in the form of a cylinder of diameter 2 2 m and height 3.5 m surmounted by a cone whose vertical angle is 90c. find total surface area of the toy

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## 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.

Click here👆to get an answer to your question ✍️ \( i + 8 \) 24. A toy is in the form of a cylinder of diameter 2\( \sqrt { 2 } \mathrm { m } \) and height 3.5\( \mathrm { m } \) sumnounte by a cone whose vertical angle is \( 90 ^ { \circ } . \) Find total surface area of the top

Question

i+8 24. A toy is in the form of a cylinder of diameter 22

m and height 3.5m sumnounte by a cone whose vertical angle is 90

∘

. Find total surface area of the top

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## A toy is in the form of a cylinder of diameter 22 𝑚 and height 3. 5 𝑚 surmounted by a cone whose vertical angle is 90°. Fund total surface area of the toy.

A toy is in the form of a cylinder of diameter 22 𝑚 and height 3. 5 𝑚 surmounted by a cone whose vertical angle is 90°. Fund total surface area of the toy.

MathematicsA toy is in the form of a cylinder of diameter 22 𝑚 and height 3. 5 𝑚 surmounted by a cone whose vertical angle is 90°. Fund total surface area of the toy.

A toy is in the form of a cylinder of diameter

2 2 – √ 22

𝑚 and height 3. 5 𝑚 surmounted by a cone whose vertical angle is 90°. Fund total surface area of the toy.

### Solution:

We have been given a toy cylinder of diameter

2 2 – √ 22

𝑚 and height 3. 5 𝑚.

By Pythagoras Theorem we know that the sum of the squares on the legs of a right triangle is equal to the square of the hypotenuse. We can see that ∠𝐶 = 90°

⇒A B 2 =A C 2 +B C 2 ⇒AB2=AC2+BC2

Let the slant height of the cone 𝐴𝐶 be 𝑥.

⇒A B 2 = x 2 + x 2 [AC=BC] ⇒(2 2 – √ ) 2 =2 x 2 ⇒x=4m ⇒x=2m

⇒AB2=x2+x2[AC=BC]⇒(22)2=2x2⇒x=4m⇒x=2m

Radius of the cylinder =

diameter 2 ⇒r= 2 2 √ 2 ⇒r= 2 – √ m

Radius of the cylinder = diameter 2⇒r=222⇒r=2m

Now, total surface area of toy = 𝑆𝑢𝑟𝑓𝑎𝑐𝑒 𝑎𝑟𝑒𝑎 𝑜𝑓 (𝑐𝑦𝑙𝑖𝑛𝑑𝑒𝑟 + 𝑐𝑜𝑛𝑒 + 𝑐𝑖𝑟𝑐𝑢𝑙𝑎𝑟 𝑏𝑜𝑡𝑡𝑜𝑚)

We know that, Surface area of cylinder = 2π𝑟ℎ

Surface area of cone = π𝑟𝑙

Area of bottom of cylinder =π

r 2

⇒ Surface area =2πrh+πrl+π

r 2 =πr(2h+l+r)

Area of bottom of cylinder =πr2⇒ Surface area =2πrh+πrl+πr2=πr(2h+l+r)

=π× 2 – √ ×(2×3.5)+2+ 2 – √ ) =π[2+9 2 – √ ] m 2

=π×2×(2×3.5)+2+2)=π[2+92] m2

Hence, the total surface area of the toy is

π[2+9 2 – √ ] m 2 π[2+92] m2

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## A top is in the form of a cylinder of diameter 2√2 and height 3.5 m surmounted by a cone whose vertical angle is 90°.

A top is in the form of a cylinder of diameter 2√2 and height 3.5 m surmounted by a cone whose ... angle is 90°. find total surface are of the toy.

## A top is in the form of a cylinder of diameter 2√2 and height 3.5 m surmounted by a cone whose vertical angle is 90°.

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