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Andhra Pradesh State Board Class 9th Maths Chapter 10 Surface Areas and Volumes Ex 10.3 Books Solutions

Board	AP Board
Materials	Textbook Solutions/Guide
Format	DOC/PDF
Class	9th
Subject	Maths
Chapters	Maths Chapter 10 Surface Areas and Volumes Ex 10.3
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AP State Syllabus 9th Class Maths Solutions 10th Lesson Surface Areas and Volumes Exercise 10.3

Question 1.
The base area of a cone is 38.5 cm Its volume is 77 cm³. Find its height.
Solution:
Base area of the cone, πr² = 38.5 cm²
Volume of the cone, V = 13 πr² h = 77
πr² = 38.5
227 r² = 38.5
r² = 38.5 x 722
r² = 12.25
r = 12.25‾‾‾‾‾√ = 3.5
V= 122 x 227 x 3.5 x 3.5 x h = 77
∴ h = 77×3×722×12.25 = 6
∴ Height of the cone = 6 cm

Question 2.
The volume of a cone is 462 m³. Its base radius is 7 m. Find its height.
Solution:
The volume of a cone”V’= 13 πr² h = 462
Radius ‘r’ = 7 m
Height = h (say)
13 x 227 x 7 x h = 462
h = 462×322×7 = 9
∴ Height = 9m

Question 3.
Curved surface area of a cone is 308 cm² and its slant height is 14 cm. Find (1) radius of the base (ii) total surface area of the cone.
Solution:
C.S.A. of the cone, πrl = 308
Slant height, l = 14 cm
i) πrl = 308; l = 14 cm
227 x r x 14 = 308
r = 30844 = 7cm

ii) T.S.A. = πrl + πr²
= πr (r + l) = 227 x 7 x (7 + 14)
= 22 x 21 = 462 cm³

Question 4.
The cost of painting the total surface area of a cone at 25 paise per cm2 is ₹176. Find the volume of the cone, if its slant height is 25 cm.
Solution:
Slant height of the cone, l = 25 cm
Total cost at the rate of 25 p/cm²
= ₹176
∴ Total surface area of the cone
= 17625 x 100 = 176 x 4 = 704cm²
But T.S.A. of the cone = πr (r + l) = 704
Thus 227r(r + 25) = 704
r(r + 25) = 704×722 = 224
r² + 25r = 224
⇒ r² + 32r – 7r – 224 = 0
⇒ r (r + 32) – 7 (r + 32) = 0
⇒ (r + 32) (r – 7) = 0
⇒ r = 7 (∵ ’r’ can’t be negative)

∴ Volume of the cone = 13 πr²h
= 13 x 227 x 7 x 7 24
= 22 x 7 x 8 = 1232cm³

Question 5.
From a circle of radius 15 cm, a sector with angle 216° is cut out and its bounding radii are bent so as to form a cone. Find its volume.
Solution:
Radius of the sector, ‘r’ = 15 cm
Angle of the sector, ‘x’ = 216°
∴ Length of the arc, l = 𝑥360 x 2πr
=2163602𝜋𝑟=35(2𝜋𝑟)
Perimeter of the base of the cone = Length of the arc
2πr of cone = =65 πr of the circle
Radius of the cone ‘r’ = 35 x 15 = 9
Radius ‘r’ of the circle = slant height l of the cone = 9 cm

= 1018.3 cm³

Question 6.
The height of a tent is 9 m. Its base diameter is 24 m. What is its slant height ? Find the cost of canvas cloth required if it costs ₹14 per sq.m.
Solution:
Height of a conical tent ‘h’ = 9 m
Base diameter = 24 m
Thus base radius ’r’= 𝑑2=242 = 12m
Cost of canvas = ₹ 14 per sq.m.
C.S.A. of the cone = πrl

Question 7.
The curved surface area of a cone is 115957 cm². Area of its base is 254 47 cm². Find its volume.
Solution:
C.S.A. of the cone = πrl

Question 8.
A tent is cylindrical to a height of 4.8 m and conical above it. The ra¬dius of the base is 4.5 m and total height of the tent is 10.8 m. Find the canvas required for the tent in square
meters.
Solution:

Radius of cylinder, l = 4.5 m
Height of the cylinder = h = 4.8 m
∴ C.S.A. of the cylinder = 2πrh
= 2 x 227 x 4.5 x 4.8
= 135.771 m²
Radius of the cone ‘r’ =
Radius of the cylinder = 4.5 m
Height of the cone ’h’ = 10.8 – 4.8 = 6 m
∴ Slant height of the cone

∴ C.S.A. of the cone = πrl
= 227 x 4.5 x 7.5
= 742.57 = 106.071m²
∴ Total canvas required
= C.S.A of cylinder + C.S.A. of cone
= 135.771 + 106.071
= 241.842 m²

Question 9.
What length of tarpaulin 3 m wide will be required to make a conical tent of height 8 m and base radius 6m? Assume that extra length of material that will be required for stitching margins and wastage in cutting is approximately 20 cm (use π = 3.14) [Note : Take 20 cm as 0.6 m²]
Solution:
Radius of the cone, r = 6 m
Height of the cone, h = 8 m

∴ C.S.A. = πrl = 3.14 x 6 x 10 = 188.4 m²
Let the length of the tarpaulin = l
∴ Area of the tarpaulin, lb = 188.4 + 0.6
= 189 m²
⇒ 3l = 189
⇒ l = 1893 = 63m

Question 10.
A joker’s cap is in the form of a right circular cone of base radius 7 cm and height 27 cm. Find the area of the sheet required to make 10 such caps.
Solution:
Radius of the cone, r = 7 cm
Height of the cone, h = 27 cm
Slant height of the cone (l)

∴ Total area of the sheet required for
10 caps = 10 x 22 778‾‾‾‾√
= 6136.383 cm²

Question 11.
Water is pouring into a conical vessel (as shown in the given figure), at the rate of 1.8 m³ per minute. How long will it take to fill the vessel?

Solution:
From the figure, diameter of the cone 5.2 m
Thus its radius ’r’ = 5.22 = 2.6 m
∴ Height of the cone = h = 6.8 m
Volume of the cone = 13 πr² h
= 13×227 x 2.6 x 2.6 x 6.8
= 1011.29621
= 48.156 m³
Quantity of water that flows per minute
= 1.8 m³
∴ Total time required = Total volume 1.8
= 48.1561.8 = 26.753
27 minutes.

Question 12.
Two similar cones have volumes 12π CU. units and 96π CU. units. If the curved surface area of smaller cone is 15π sq.units, what is the curved surface area of the larger one?
Solution:

πrl = 15 π
𝑟(𝑟2+ℎ2)‾‾‾‾‾‾‾‾‾√=15
Squaring on both sides
r² (r² + h²) = 15 x 15
= 3 x 5 x 3 x 5
= 3 x 3 x 25
r²(r² + h²) = 3²(3² + 4²)
∴ r = 3 cm, h = 4 cm
C.S.A. = π x 3 x (32+42‾‾‾‾‾‾‾√) = 15π
13πr²H = 96π
3×3×H3 = 96
∴ H = 963 = 32 units

AP Board Textbook Solutions PDF for Class 9th Telugu

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