Question

For the cuboidal box to satisfy certain requirements , its length must be 3m greater than its breadth and its height is 2m less than its breadth.
i) If breadth is taken as x , which of the following represents volume.
a. x³ - 3x -6 b. x³ + x² - 6x c. x³ - 6x² - 6x d. x³ + x - 6
ii) Area of the paper sheet used to make the box is
a. x² - 5x - 6 b. 6x² + 3x - 4 c. x³ - 6 x² - 6x d. 6x² + 4x - 12
iii) If its volume is 18 units then its length is
a. 6 b. 3 c. 4 d. 2
iv) Find the cost used to make this box ( of volume 18 ) if the sheet is 100 rs per square unit
a. 5400 b. 10800 c. 2700 d. 3400
v) If its volume is 56 units then its height is
a. 1 b. 2 c. 3 d. 4

Answer 1

SOLUTION

TO EVALUATE

For the cuboidal box to satisfy certain requirements , its length must be 3m greater than its breadth and its height is 2m less than its breadth.

i) If breadth is taken as x , which of the following represents volume.

a. x³ - 3x -6

b. x³ + x² - 6x

c. x³ - 6x² - 6x

d. x³ + x - 6

ii) Area of the paper sheet used to make the box is

a. x² - 5x - 6

b. 6x² + 3x - 4

c. x³ - 6x² - 6x

d. 6x² + 4x - 12

iii) If its volume is 18 units then its length is

a. 6

b. 3

c. 4

d. 2

iv) Find the cost used to make this box ( of volume 18 ) if the sheet is 100 rs per square unit

a. 5400

b. 10800

c. 2700

d. 3400

v) If its volume is 56 units then its height is

a. 1

b. 2

c. 3

d. 4

EVALUATION

Here breadth = x

∴ Length = x + 3

∴ Height = x - 2

(i) Volume

$\sf{ = (x + 3)(x)(x - 2)}$

$\sf{ = (x + 3)( {x}^{2} - 2x) }$

$\sf{ = {x}^{3} - 2 {x}^{2} + 3 {x}^{2} - 6x }$

$\sf{ = {x}^{3} + {x}^{2} - 6x }$

Hence the correct option is b. x³ + x² - 6x

(ii) Area of the paper sheet used to make the box

= 2 [ x(x+3) + x(x-2) + ( x + 3) (x-2)]

= 2[ x² + 3x + x² - 2x + x² + 3x - 2x - 6 ]

= 2 (3x² + 2x - 6)

= 6x² + 4x - 12

Hence the correct option is d. 6x² + 4x - 12

(iii) Here volume is 18 units

∴ (x+3)x(x-2) = 18

∴ (x+3)x(x-2) = 6 × 3 × 1

Comparing both sides we get x = 3

∴ Length = ( 3 + 3 ) = 6 cm

Hence the correct option is a. 6

(iv) When x = 3

6x² + 4x - 12

= 6(3)² + 4.(3) - 12

= 54 + 12 - 12

= 54

∴ Required cost = Rs ( 54 × 100 ) = Rs 5400

Hence the correct option is a. 5400

(v) Here volume is 56 units

∴ (x+3)x(x-2) = 56

∴ (x+3)x(x-2) = 7 × 4 × 2

Comparing both sides we get x = 4

∴ Height = x - 2 = 4 - 2 = 2

Hence the correct option is b. 2

━━━━━━━━━━━━━━━━

Learn more from Brainly :-

1. In an equilateral triangle, the ratio of the radii of incircle, circumcircle and excircle is

https://brainly.in/question/10164855

2. find the circumcentre of A(2,-5),B(6,8) C(2,8)

https://brainly.in/question/29572481

Answer 2

$\huge\underline{\bf \orange{AnSweR :}}$

(i) Volume

→ (x+3)(x)(x−2)

→ (x+3)(x² −2x)

→ x³ −2x² + 3x² −6x

→ x³ +x² −6x

Hence the correct option is b. x³ + x² - 6x

(ii) Area of the paper sheet used to make the box

→ 2 [ x(x+3) + x(x-2) + ( x + 3) (x-2)]

→ 2[ x² + 3x + x² - 2x + x² + 3x - 2x - 6 ]

→ 2 (3x² + 2x - 6)

→ 6x² + 4x - 12

Hence the correct option is d. 6x² + 4x - 12

(iii) Here volume is 18 units

∴ (x+3)x(x-2) = 18

∴ (x+3)x(x-2) = 6 × 3 × 1

Comparing both sides we get x = 3

∴ Length = ( 3 + 3 ) = 6 cm

Hence the correct option is a. 6

(iv) When x = 3

6x² + 4x - 12

= 6(3)² + 4.(3) - 12

= 54 + 12 - 12

= 54

∴ Required cost = Rs ( 54 × 100 ) = Rs 5400

Hence the correct option is a. 5400

(v) Here volume is 56 units

∴ (x+3)x(x-2) = 56

∴ (x+3)x(x-2) = 7 × 4 × 2

Comparing both sides we get x = 4

∴ Height = x - 2 = 4 - 2 = 2

Hence the correct option is b. 2