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Because 2Pi x r x L is the curved surface of a cylinder.
Clearly a cylinder have more surface area than a cone of same height and radius.
The surface of the cone is Pi x r x S where S is the slope length, so the cylinder has approximately double the surface area (note S is longer than L).
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What is the formulae for finding the curved surface area of a frustum of a cone?
The frustum of a cone looks like a plant pot and its curved surface area is: pi*(r1+r2)*l whereas r1 is the top radius and r2 is the bottom radius with l being its slanted length.
What is the formula to find the area of a cone?
Base surface = pi*r2 Curved surface = pi*r*l where l is the slant height If the vertical height (h) is given rather than the slant height, then use Pythagoras: l2 = h2 + r2
How do you find the surface area of a cone?
A cone has two surfaces, lateral surface and its circular surface at the base.The surface area of a cone is the sum of the areas of these two surfaces, i.e. (1) area of the lateral surface and (2) area of its base.Let us consider a right circular cone to find its surface area.The lateral surface area of a right circular cone is π r lwhere,r is the radius of the circle at the bottom of the cone, andl is the lateral height of the coneThe surface area of the bottom circle of a cone is the same as for any circle, π r2Thus the total surface area of a right circular cone is: π r l + πr2 OR π r (l + r)
The formula for suface area of a cone?
Since the base of a cone is a circle, we substitute 2πr for p and πr2 for B where r is the radius of the base of the cylinder. So, the formula for the lateral surface area of a right cone is L. S. A. = πrl, where l is the slant height of the cone.
What is the derivation of the total surface area of a cone?
IIr( l + r ) where II is 22/7
How do you find the curved surface area of cone?
Suppose you have a cone with slant height='l' and base radius 'r' and perpendicular height 'h' Curved surface area of COne=pi*r*l =pi*r*(squareroot(r2+h2))
Area of a cone?
The surface area of a cone is: Curved Surface: pi X the radius X L (L is the slant of the cone pointing to the tip. \ ) Flat Area/Base: pi X the radius *squared* easy.
Why is the curved surface of cone not 2pi x r x l when the circumference is 2 x pi x r and L is the slant height that moves through this distance?
Good question. Firstly, I'm assuming you are referring to a regular cone (i.e one with the same slope on all sides, as opposed to one where the uppermost "tip" is pushed off centre).The area 2*pi*radius* length does give you a "surface", but it is based on the base measurements of the cone - it is the surface that would be created if you were to extend the curved surface straight upwards from the base of the cone (i.e creating a cylinder, not a cone).A cone clearly has less curved surface area than a cylinder - in fact, it has half the surface area of the equivalent cylinder. So the equation is pi*radius*slant height. (i.e not 2*pi*radius*slant height).
What is the formulae for finding the curved surface area of a frustum of a cone?
The frustum of a cone looks like a plant pot and its curved surface area is: pi*(r1+r2)*l whereas r1 is the top radius and r2 is the bottom radius with l being its slanted length.
How do you find the lateral surface area of a cone?
pi times l times r (r and l are the radius and slant height, respectively)This can be derived by using a ratio (area/circumference) of the circle with radius L (slant height) with the ratio of the arc (arc-area/arclength). It should look something like this.(pi*l^2)/(2pi*l) = (arc-area)/(2pi*r)
What is the formula to find the area of a cone?
Base surface = pi*r2 Curved surface = pi*r*l where l is the slant height If the vertical height (h) is given rather than the slant height, then use Pythagoras: l2 = h2 + r2
How do you find the surface area of a cone?
A cone has two surfaces, lateral surface and its circular surface at the base.The surface area of a cone is the sum of the areas of these two surfaces, i.e. (1) area of the lateral surface and (2) area of its base.Let us consider a right circular cone to find its surface area.The lateral surface area of a right circular cone is π r lwhere,r is the radius of the circle at the bottom of the cone, andl is the lateral height of the coneThe surface area of the bottom circle of a cone is the same as for any circle, π r2Thus the total surface area of a right circular cone is: π r l + πr2 OR π r (l + r)
The formula for suface area of a cone?
Since the base of a cone is a circle, we substitute 2πr for p and πr2 for B where r is the radius of the base of the cylinder. So, the formula for the lateral surface area of a right cone is L. S. A. = πrl, where l is the slant height of the cone.
What is the derivation of the total surface area of a cone?
IIr( l + r ) where II is 22/7
What is the equation for the Surface Area of a cylinder?
If the cylinder has radius R and length L , the curved part of the surface has area 2piRL and each of the ends has area piR^2. The total surface area is the sum of the curved part plus two ends.
What is the lateral surface area of a right cylinder?
The lateral area of a right cylinder is curved surface that connects the two bases. The surface area is the total area of the curved surface and the bases.Lateral Area: The lateral area of a right cylinder with radius r and height h is L = 2pirh.Surface Area: The surface area of a right cylinder with lateral area L and base area B is S = L + 2B, or S = 2pirh + 2pir^2.
How do you find the hight of a cone?
A cone is a 3 dimensional shape and therefore does not have an "area" the way a circle or a square does. 3 dimensional shapes such as cones can have "surface area" and "cross-sectional area". Note that 3 dimensional shapes can have an infinite number of different cross sectional areas because you can define an infinite number of cross sections. So I'll assume you are asking about the surface area of a cone. The surface area is the sum of the area of the base (circle) and the actual cone part. Let's assume the base has a radius "r" and the length of the "angled" part of the cone (from the outside of the base to the peak of the cone) is "L". So the base has an area of: (pi)*r^2 (where ^ means "to the power of") and the cone part has a surface area of: (pi)*r*L Therefore the total surface area of the cone is: base + cone (pi)*r^2 + (pi)*r*L
