SECTION - II
17. Tata Steels is going to make frames as part of a new warehouse they are sedung
for amazon fulfilment projects. To manage detailing, fabrication and construction of
framing projects can be challenging. For which, they are using a 3D CAD software to crets
a constructible model that includes the relevant information such as dimensions of the
warehouse and materials needed.
The frame will have a solid base and will be cut out of a piece of steel, and to keep the
weight down, the final area of the frame should be 28 sq cm.
In order to input the right values in the CAD software, the engineer needs to calculate some
basic things.
6 cm
11 cm
On the basis of the above information, answer any four of the following questions
(A) If the width of the frame is 'X' cm, then the dimensions of the outer frame are:
(a) (11 + x) and (6 + x)
(b) (11 - x) and (6 - x)
(C) (11 + 2x) and (6 + 2x)
(d) (11 - 2x) and (6 - 2x)
(B) Area of the metal sheet (in sq cm) before cutting is:
(a) 4x2 + 34x + 66
(b) x2 + 17x + 66
(c) 5x2 + 30
(d) 10(x2 + 15x + 4)
(C) Area of metal sheet (in sq cm) after cutting out the 11 cm x 6 cm inside, is:
(a) x2 + 17x
(b) 12x2 + 51
(C) 4x2 + 30
(d) 4x2 + 34x
(D) If the area of the frame is 28 sq cm, the value of 'X' is:
(a) 0.8 cm
(b) 1.3 cm
(C) 1.4 cm
(d) 1.1 cm
(E) The perimeter of the frame is:
(a) 30.8 cm
(b) 37.2 cm
(c) 40.4 cm
(d) 27.6 cm
Answers
Answer:
I am a bit more, please 4 the
A) If the width of the frame is 'X' cm, then the dimensions of the outer frame are:
(a) (11 + x) and (6 + x)
(b) (11 - x) and (6 - x)
(C) (11 + 2x) and (6 + 2x)
(d) (11 - 2x) and (6 - 2x)
Answer :-
→ Length of outer frame = 11 + 2 * width = (11 + 2x) cm.
→ Breadth of outer frame = 6 + 2 * width = (6 + 2x) cm.
so, the dimensions of the outer frame are (C) (11 + 2x) and (6 + 2x) .
(B) Area of the metal sheet (in sq cm) before cutting is:
(a) 4x2 + 34x + 66
(b) x2 + 17x + 66
(c) 5x2 + 30
(d) 10(x2 + 15x + 4)
Answer :-
→ Area of metal sheet = Length * Breadth = (11 + 2x) * (6 + 2x) = 11*6 + 11*2x + 2x*6 + 2x*2x = 66 + 22x + 12x + 4x² = 4x² + 34x + 66 (a) (Ans.)
(C) Area of metal sheet (in sq cm) after cutting out the 11 cm x 6 cm inside, is:
(a) x2 + 17x
(b) 12x2 + 51
(C) 4x2 + 30
(d) 4x2 + 34x
Answer :-
→ Area of metal sheet (in sq cm) after cutting out the 11 cm x 6 cm inside = Area of metal sheet - Area of cutting = (4x² + 34x + 66) - (11 * 6) = 4x² + 34x + 66 - 66 = 4x² + 34x (d) (Ans.)
(D) If the area of the frame is 28 sq cm, the value of 'X' is:
(a) 0.8 cm
(b) 1.3 cm
(C) 1.4 cm
(d) 1.1 cm
Answer :-
→ 4x² + 34x = 28
→ 4x² + 34x - 28 = 0
→ 2(2x² + 17x - 14) = 0
→ 2x² + 17x - 14 = 0
→ 2x² + 17x - 14 = 0
solving this we get,
→ x ≈ 0.8 cm (a) (Ans.)
(E) The perimeter of the frame is:
(a) 30.8 cm
(b) 37.2 cm
(c) 40.4 cm
(d) 27.6 cm
Answer :-
→ Perimeter = 2(L + B) = 2(11 + 2x + 6 + 2x) = 2(17 + 4x) = 34 + 8x = 34 + 8*0.8 = 34 + 6.4 = 40.4 cm (c) (Ans.)
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