PROBLEMS ON SURFACE AREA OF CONE
Problem 1 :
If the vertical angle and the radius of the right circular cone are 60 degree and 15 cm respectively, then find its slant height and curved surface area.
Solution :
Vertical angle of the right circular cone = 60°
radius of the cone (r) = 15 cm
In the triangle ABC, ∠ABC = 30°
BC = 15 cm
Opposite side (BC) = 15 cm
Adjacent side (AB) = ?
Hypotenuse side (AC) = ?
here, we need to find the measurement of the side AC. So we have to use sinθ.
sin θ = Opposite side/Hypotenuse side
sin 30° = BC/AC
(1/2) = 15/AC
AC = 30 cm
Slant height (L) = 30 cm
Curved surface area of cylinder = π r l
= π ⋅ 15 ⋅ 30
= 450 π cm2
So, curved surface area of cone is 450 π cm2
Problem 2 :
If the circumference of the base of the solid right circular cone is 236 and its slant height is 12 cm, find its curved surface area.
Solution :
Circumference of the base = 236 cm
Slant height (L) = 12 cm
2 Π r = 236
Πr = 236/2
Π r = 118
Curved surface area of cone = Π r l
= 118 (12)
= 1416 cm2
So, curved surface area of cone is 1416 cm2
Problem 3 :
A heap of paddy is in the form of a cone whose diameter is 4.2 m and height is 2.8 m. If the heap is to be covered exactly by a canvas to protect it from rain, then find the area of the canvas needed.
Solution :
Diameter of heap of paddy = 4.2 m
r = 4.2/2
r = 2.1 m
height of paddy (h) = 2.8 m
l2 = r2+h2
l = √(2.1)2+(2.8)2
l = √(4.41+7.84)
l = √12.25
l = √(3.5 ⋅3.5)
l = 3.5 cm
Curved surface area of heap of paddy = Π r l
= (22/7) ⋅ 2.1 ⋅ 3.5
= 22 ⋅ 2.1 ⋅ 0.5
= 23.1 cm2
So, curved surface area of paddy is 23.1 cm2.
Problem 4 :
The central angle and radius of a sector of a circular disc are 180 degree and 21 cm respectively. If the edges of the sector are joined together to make a hollow cone, then find the radius of the cone.
Solution :
The cone is being created by joining the radius. So the radius of the sector is going to be the slant height of the cone.
Slant height L = 21 cm
Arc length of the sector = Circumference of the base of the cone
Length of arc = (θ/360) ⋅ 2Π R
Here R represents radius of the sector
= (180/360) ⋅ 2 ⋅ (22/7) ⋅ 21
= (1/2) ⋅ 2 ⋅ 22 ⋅ 3
= 66 cm
So, circumference of the base of the cone = 66
2 Π r = 66
2 ⋅ (22/7) ⋅ r = 66
r = 10.5 cm
So, radius of the cone is 10.5 cm.
Problem 5 :
Radius and slant height of a solid right circular cone are in the ratio 3:5. If the curved surface area is 60Π cm², then find its radius and slant height.
Solution :
Radius and slant height of a solid right circular cone are in the ratio 3:5.
r : L = 3 : 5
r / L = 3/5
r = 3L/5
Curved surface area of cone = 60 Πcm²
Π r L = 60Π
Π ⋅ (3L/5) ⋅ L = 60Π
l2 = 60 Π ⋅ (1/Π) ⋅ (5/3)
l2 = 60 ⋅ (5/3)
l2 = 100
l = 10 cm
r = 3(10)/5
r = 30/5
r = 6 cm
So, radius and slant height of cone are 6 cm and 10 cm respectively.
Problem 6 :
A sector containing an angle of 120 degree is cut off from a circle of radius 21 cm and folded into a cone. Find the curved surface area of a cone.
Solution :
The cone is being created by joining the radius. So the radius of the sector is going to be the slant height of the cone.
Slant height (l) = 21 cm
Arc length of the sector = Circumference of the base of the cone
Length of arc = (θ/360) ⋅ 2Π R
Here R represents radius of the sector
= (120/360) ⋅ 2 ⋅ (22/7) ⋅ 21
= (1/3) ⋅ 2 ⋅ 22 ⋅ 3
= 44 cm
So, circumference of the base of the cone = 44
2Πr = 44
2 ⋅ (22/7) ⋅ r = 44
r = 7 cm
Now, we need to find the curved surface area of cone
Curved surface area of cone = Πrl
= (22/7) x 7 x 21
= 462 cm2
So, curved surface area is 462 cm2.
Apart from the stuff given in this section, if you need any other stuff in math, please use our google custom search here.
If you have any feedback about our math content, please mail us :
v4formath@gmail.com
We always appreciate your feedback.
You can also visit the following web pages on different stuff in math.
WORD PROBLEMS
Word problems on simple equations
Word problems on linear equations
Word problems on quadratic equations
Area and perimeter word problems
Word problems on direct variation and inverse variation
Word problems on comparing rates
Converting customary units word problems
Converting metric units word problems
Word problems on simple interest
Word problems on compound interest
Word problems on types of angles
Complementary and supplementary angles word problems
Trigonometry word problems
Markup and markdown word problems
Word problems on mixed fractrions
One step equation word problems
Linear inequalities word problems
Ratio and proportion word problems
Word problems on sets and venn diagrams
Pythagorean theorem word problems
Percent of a number word problems
Word problems on constant speed
Word problems on average speed
Word problems on sum of the angles of a triangle is 180 degree
OTHER TOPICS
Time, speed and distance shortcuts
Ratio and proportion shortcuts
Domain and range of rational functions
Domain and range of rational functions with holes
Graphing rational functions with holes
Converting repeating decimals in to fractions
Decimal representation of rational numbers
Finding square root using long division
L.C.M method to solve time and work problems
Translating the word problems in to algebraic expressions
Remainder when 2 power 256 is divided by 17
Remainder when 17 power 23 is divided by 16
Sum of all three digit numbers divisible by 6
Sum of all three digit numbers divisible by 7
Sum of all three digit numbers divisible by 8
Sum of all three digit numbers formed using 1, 3, 4
Sum of all three four digit numbers formed with non zero digits
Recent Articles
-
Volume and Surface Area of Composite Solids Worksheet
Jan 20, 21 10:31 AM
Volume and Surface Area of Composite Solids Worksheet
-
Combination of Solid Shapes Problems
Jan 20, 21 09:46 AM
Combination of Solid Shapes Problems
-
Example Problems on Surface Area with Combined Solids
Jan 20, 21 02:51 AM
Example Problems on Surface Area with Combined Solids
