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## AP Board Class 8 Maths Chapter 14 Surface Areas and Volume InText Questions Textbook Solutions PDF: Download Andhra Pradesh Board STD 8th Maths Chapter 14 Surface Areas and Volume InText Questions Book Answers

 AP Board Class 8 Maths Chapter 14 Surface Areas and Volume InText Questions Textbook Solutions PDF: Download Andhra Pradesh Board STD 8th Maths Chapter 14 Surface Areas and Volume InText Questions Book Answers

## Andhra Pradesh State Board Class 8th Maths Chapter 14 Surface Areas and Volume InText Questions Books Solutions

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## AP Board Class 8th Maths Chapter 14 Surface Areas and Volume InText Questions Textbooks Solutions with Answer PDF Download

Find below the list of all AP Board Class 8th Maths Chapter 14 Surface Areas and Volume InText Questions Textbook Solutions for PDF’s for you to download and prepare for the upcoming exams:

Question 1.
Find the total surface area of the following cuboid. [Page No. 298]

i) l = 4 cm, b = 4 cm, h = 10 cm.
The total surface area of a cuboid = 2 (lb + bh + lh)
= 2 (4 × 4 + 4 × 10 + 4 × 10) = 2(16 + 40 + 40)
= 2 × 96
= 192 Sq. cms.

ii) l = 6 cm, b = 4 cm, h = 2 cm.
The total surface area of a cuboid = 2 (lb + bh + lh)
= 2(6 × 4 + 4 × 2 + 6 × 2)
= 2 (24 + 8 + 12)
= 2 × 44
= 88 sq. cms.

Question 2.
Let us find the volume of a cuboid whose length, breadth and height are 6 cm, 4 cm and 5 cm respectively. [Page No. 287]

Let place 1 cubic centimeter blocks along the length of the cuboid. How many blocks can we place along the length? 6 blocks, as the length of the cuboid is 6 cm.
How many blocks can we place along its breadth? 4 blocks, as the breadth of the cuboid is 4 cm. So there are 6 × 4 blocks can be placed in a layer.
How many layers of blocks can be placed in the cuboid? 5 layers, as the height of the cuboid is 5 cm. Each layer has 6 × 4 blocks. So, all the 5 layers will have 6 × 4 × 5 blocks i.e. length × breadth × height.
This discussion leads us to the formula for the volume of a cuboid.
Volume of a cuboid = length × breadth × height [Page No. 305]
The dimensions of a cuboid are 6 cm, 4 cm, 5 cm respectively.
∴ Volume (V) = lbh
= 6 × 4 × 5.
= 120 cm3

Question 3.
Arrange 64 unit cubes in as many ways as you can to form a cuboid. Find the surface area of each arrangement. Can solid cuboid of same volume have same surface area? [Page No. 306]
No. of cuboids are formed using 64 unit cubes
64 = 1 × 64 ……. (1)
= 2 × 32 …….. (2)
= 4 × 16 …….. (3)
1) l = 64 cm, b = 1 cm, h = 1 cm.
The total surface area of a cuboid, A = 2 (lb + bh + lh)
= 2 (64 × 1 + 1 × 1 + 1 × 64)
= 2 (64 + 1 + 64)
= 2 × 129
= 258 Sq. cm.

2) l = 32 cm, b = 2 cm, h = 1 cm.
A = 2 (lb + bh + lh)
= 2 (32 × 2 + 2 × 1 + 32 × 1)
= 2 (64 + 2 + 32)
= 2 × 98 = 196 Sq. cm.

3) l = 16 cm, b = 4 cm, h = 1 cm.
A = 2 (lb + bh + lh)
= 2 (16 × 4 + 4 × 1 + 16 × 1)
= 2 (64 + 4 + 16)
= 2 × 84 = 168 Sq. cm.

No, the volume of a cuboid is not same as the surface area of a cuboid.

Try These

Question 1.
Find the surface area of cube ‘A’ and lateral surface area of cube ‘B’. [Page No. 300]

a = 10 cm.
The total surface area of a figure ‘A’ = 6a2
= 6 × (10)2
= 6 × 100 = 600 Sq. cm.
Lateral surface area of a figure ‘B’ – 4a2
= 4 × (8)2 [∵ a = 8 cm.]
= 4 × 64 = 256 Sq. cm.

Question 2.
Two cubes each with side ‘b’ are joined to form a cuboid as shown in the given fig. What is the total surface area of this cuboid? [Page No. 300]

Total surface area of a cuboid = 2 (lb + bh + lh)
= 2 (2b × b + b × b + 2b × b)
= 2 (2b2 + b2 + 2b2)
= 2(5b2) = 10b2 Sq. cm.

Question 3.
How will you arrange 12 cubes of equal lengths to form a cuboid of smallest surface area? [Page No. 300]

We can’t obtain the least total surface area by arranging 12 cubes by side by side.

∴ A = 2 (lb + bh + lh)
= 2 (12 × 1 + 1 × 1 + 12 × 1)
= 2 (12 + 1 + 12)
= 2 × 25 = 50 Sq. cm.
We can obtain the least total surface area by arranging 3 cubes by 4 cubes.
∴ A = 2 (lb + bh + lh)
= 2 (3 × 1 + 1 × 4 + 3 × 4) (∵ l = 3; b = 1; h = 4)
= 2 (3 + 4 + 12)
= 2 × 19
= 38 Sq. cm.

Question 4.
The surface area of a cube of 4 × 4 × 4 dimensions is painted. The cube is cut into 64 equal cubes. How many cubes have
(a) 1 face painted? (b) 2 faces painted? (c) 3 faces painted? (d) no face painted? [Page No. 300]
If the 4 × 4 × 4 cube is divided into 64 equal cubes then the length of its each side = 1 unit.

[∵ 4×4×464 = 1]
a) No.of cubes (a = 4) have painted 1 face = 6(a – 2)2 = 6(4 – 2)2 = 6 × 4 = 24
b) No.of cubes have painted 2 faces = 12(a – 2) = 12(4 – 2) = 24
c) No.of cubes have painted 3 faces = 4 × a = 4 × 2 = 8
d) No.of cubes have painted no faces = (a – 2)3 = (4 – 2)3 = (2)3 = 8

Think, Discuss and Write

Question 1.
Can we say that the total surface area of cuboid = lateral surface area + 2 × area of base. [Page No. 299]
Total surface area of a cuboid = L.S.A + 2 × Area of base
= 2h (l + b) + 2 × lb
= 2lh + 2bh + 2lb
= 2 (lb + bh + lh)
We can conclude that total surface area of a cuboid = L.S.A + 2 × Area of base

Question 2.
If we change the position of cuboid from Fig. (i) to Fig. (ii) do the lateral surface areas become equal? [Page No. 299]

There will be no change in the L.S.A of a cuboid if its positions are changed.

Question 3.
Draw a figure of cuboid whose dimensions are l, b, h are equal. Derive the formula for LSA and TSA. [Page No. 299]

Lateral surface area of a cuboid
= 4 × (areas of 4 faces)
= 2 (l × h) + 2 × (b × h) (1 + 2 + 3 + 4 faces)
= 2h(l + b) sq.units (1 = 3, 4 = 2)
∴ Total surface area of a cuboid
= 4 × (Area of 4 faces) + (Areas of upper & lower faces)
= 2h (l + b) + 2 (lb)
= 2lh + 2bh + 27b
= 2 (lb + bh + lh) sq.units

## Andhra Pradesh Board Class 8th Maths Chapter 14 Surface Areas and Volume InText Questions Textbooks for Exam Preparations

Andhra Pradesh Board Class 8th Maths Chapter 14 Surface Areas and Volume InText Questions Textbook Solutions can be of great help in your Andhra Pradesh Board Class 8th Maths Chapter 14 Surface Areas and Volume InText Questions exam preparation. The AP Board STD 8th Maths Chapter 14 Surface Areas and Volume InText Questions Textbooks study material, used with the English medium textbooks, can help you complete the entire Class 8th Maths Chapter 14 Surface Areas and Volume InText Questions Books State Board syllabus with maximum efficiency.

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