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
Mohammed
Guys, does anyone know the answer?
get 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 from screen.
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
Open in App Solution Verified by Toppr
Was this answer helpful?
39 9
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
Related content
Matrices and Determinants_mathematics
Critical Points Solved Examples
Type of relations_mathematics
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°.
← Prev Question Next Question →
1 Answer
← Prev Question Next Question →
Find MCQs & Mock Test
JEE Main 2024 Test Series
NEET Test Series
Class 12 Chapterwise MCQ Test
Class 11 Chapterwise Practice Test
Class 10 Chapterwise MCQ Test
Class 9 Chapterwise MCQ Test
Class 8 Chapterwise MCQ Test
Class 7 Chapterwise MCQ Test
Guys, does anyone know the answer?