9th Maths 13.3
Chapter 13
Surface Areas and Volumes
NCERT Class 9th solution of Exercise 13.1
NCERT Class 9th solution of Exercise 13.2
NCERT Class 9th solution of Exercise 13.4
NCERT Class 9th solution of Exercise 13.5
NCERT Class 9th solution of Exercise 13.6
NCERT Class 9th solution of Exercise 13.7
NCERT Class 9th solution of Exercise 13.8
NCERT Class 9th Projects
Exercise 13.3
Assume π=227, unless stated otherwise.
Q1. Diameter of the base of a cone is 10.5cm and its slant height is10cm. Find its curved surface area.
Sol. :
Given:
Radius of base is r=10.52cm
Slant height is l=10cm
To Find:
Curved Surface Area of Cone.
Solve:
Curved Surface Area of Cone=πrl
=227×10.52×10
=11×1.5×10
=165.0cm2
Answer:
The curved Surface Area of the Cone is 165.0cm2.
Q2. Find the total surface area of a cone, if its slant height is 21m and diameter of its base is 24m.
Sol. :
Given:
Radius of base is r=242=12m
The slant height is l=21m
To Find:
The total surface area of a cone.
Solve:
Total Surface Area of cone=πr(r+l)
=227×12×(12+21)
=227×12×33
=227×396
=1244.57m2
Answer:
The total Surface Area of the Cone is 1244.57m2.
Q3. Curved surface area of a cone is 308cm2and its slant height is 14cm. Find
i) radius of the base and ii) total surface area of the cone.
Sol. :
Given:
The curved Surface Area of the Cone is 308cm2
Slant height is l=14cm
To Find:
i) radius of the base
ii) total surface area of the cone
Solve:
i) Curved Surface Area of Cone=πrl
308=227×r×14
r=308×722×14
r=15411×2
r=7711
r=7
Answer:
The radius of the base is 7cm.
ii) Total Surface Area of the Cone=πr(r+l)
=227×7(7+14)
=22×21
=462cm2
Answer:
The total Surface Area of the Cone is 462cm2.
Q4. A conical tent is 10m high and the radius of its base is 24m. Find
i) slant height of the tent.
ii) cost of the canvas required to make the tent if the cost of 1m2 canvas is ₹70.
Sol. :
Given:
The height of Cone is h=10m
The radius of the base is r=24m
Rate ₹70perm2
To Find:
i) Slant height of the tent.
ii) Cost of the canvas.
Solve:
Slant height of Conel=√h2+r2
l=√(10)2+(24)2
l=√100+576
l=√676
l=26
Answer:
The slant height of the tent is 26m.
ii) Area of Cone=πrl
=227×24×26
=1961.14m2
Cost of the Canvas=Area×Rate
=1961.14×70
=₹137280
Answer:
The cost of the canvas is ₹ 137280.
Q5. What length of tarpaulin 3m wide will be required to make a conical tent of height 8m and base radius 6m? Assume that the extra length of material that will be required for stitching margins and stage in cutting is approximately 20cm (Use π=3.14).
Sol. :
Given:
The breadth of Tarpaulin B=3m
The height of Conical Tent h=8m
The radius of Base r=6m
Extra length =20cm=0.2m
To Find:
Length of Tarpaulin.
Solve:
Slant height l=√r2+h2
l=√(6)2+(8)2
l=√36+64
l=√100
l=10m
Area of the Tarpaulin=πrl
=3.14×6×10
=188.4m2
Length of Tarpaulin=Area of TarpaulinBreadth of Tarpaulin
=188.43
62.8m
Total Length of Tarpaulin =Length of Tarpaulin + Extra Lenght
=62.8+0.20
=63m
Answer:
The Total Length of a Tarpaulin is 63m
Q6. The slant height and base diameter of a conical tomb are 25m and 14m respectively. Find the cost of white-washing its curved surface at the rate of ₹210 per `100m^2.
Sol. :
Given:
The slant height is l=25m
The radius of the Conical Tomb is 142=7m
The rate of White-Washing is ₹210 per 100m2
To Find:
Cost of White-Washing.
Solve:
Curved Surface Area of Cone=πrl
=227×25×7
=550m2
Cost of White- Washing =Area×Rate
=₹550×210100
=₹1155
Answer:
Cost of White-Washing₹ 1155}`.
Q7. A joker's cap is in the form of a right circular cone of base radius 7cm and height 24cm. Find the area of the sheet required to make 10such caps.
Sol. :
Given:
The radius of Cone is r=7cm
Height of Cone is h=24cm
To Find:
Area of the sheet.
Solve:
Slant height l=√r2+h2
l=√(7)2+(24)2
l=√49+576
l=√625
l=25cm
sheet required for one cap = Curved Surface Area of Cone
=πrl
=227×7×25
=22×25
=550cm2
Sheet required for 10 such caps =550×10
=5500cm2
Answer:
Sheet required for 10 such caps 5500cm2.
Q8. A bus stop is barricaded from the remaining part if the road, by using 50 hollow cones made of recycled cardboard. Each cone has a base diameter of 40cm and height 1m. If the outer side of each of the cones is to be painted and the cost of painting is ₹12perm2, what will be the cost of painting all these cones? (Use π=3.14 and takes √1.04=1.02).
Sol. :
Given:
Radius of base is r=402=20cm=0.2m
Height of the Cone h=1m
The rate of paint is ₹12 per m2
To Find:
Total Cost of paint.
Solve:
Slant height of Cone l=√r2+h2
l=√(0.2)2+(1)2
l=√0.04+1
l=√1.04
l=1.02m
Curved Surface Area of a Cone =πrl
=227×0.2×1.02
Curved Surface Area of 50 Cones =50×πrl
=50×227×0.2×1.02
Cost of Painting =Area×Rate
=₹50×227×0.2×1.02×12
=₹384.68(approx.)
Answer:
Total Cost of Paint ₹ 384.68 (approx).
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