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# Cylinder,Sphere and cone

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Volume ,surface area and exercise about Cylinder,Sphere and cone

Volume ,surface area and exercise about Cylinder,Sphere and cone

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• 1. Volume and Surface Are of Cylinder, Sphere, and Cone
• 2. Cone
+
+
=
A Coneis a three dimensional solid with a circular base and a curved surface that gradually narrows to a vertex.
• 3. FORMULAS of a cone
Surface Area : Area of base + lateral surface face
: ∏r2 + ∏rs
: ∏r (r + s)
Lateral Surface Area : ∏rs
Volume of a cone :
• 4. 1. Find the Volume of Cone
Find the volume of a cone with a radius diameter=7cmand height=10cm, taking p=22/7
Volume of a Cone
= (1/3) pr2h
= (1/3)(22/7)(3.5)2(10)
= 11 x 3.5 x 10
Volume= 385cm3
• 5. 2. Find the lateral surface area
The radius of cone’s base is 3cm and the height of the cone is 4cm, taking p = 3.14.
Lateral Surface Area = prs (slant height).
S2 = r2 + t2 The lateral surface area = prs
= 32 + 42 = 3.14 x 3 x 5
= 9 + 16 = 47.1 cm2
S2 = √25
S = 5cm
• 7. Find the Surface Area of a Cone
Find the area of a cone with a radius r=3 m and height h=4 m.
r = the radius h = the height l = the slant height
Use thePythagorean Theorem to find l
l 2 = r2 + h2
l 2= (3)2 + (4)2
l 2= 25
l = 5
Total Surface Area of a Cone
= pr2 + Lateral surface area
= pr2 + prs
= 3.14(3)2 + 3.14(3)(5)
= 75.36 m2
• 8. Volume of sphere
r
h
r
Volume of a Sphere = 2 x (2 x volume of a cone)
= 4 x 1/3∏r2t  substitute t = r
= 4 x 1/3 ∏r2 x r
Volume of a Sphere = 4/3 ∏r3
• 9. Question for volume of a sphere
9
The radius of a sphere is 7 cm. Find the volume of the sphere if we have ∏=22/7!
V= 4/3 ∏r3
V= 4/3. 22/7. 73
V= 1473
Thus, the volume of the sphere is 1473 cm3.
• 10. Volume of a Cylinder = base x height = pr2h
= 3.14(1)2(2)
= 6.28 m3
• 11. Volume of a cylinder
Find the volume of a cylinder with a radius r=1 m and height h=2 m.
Know : r = 1 m h = 2 m