3 Mark Question

Question 13 Marks

A matchbox is 4 cm long, 2.5 cm broad and 1.5 cm in height. Its outer sides are to be covered exactly with craft paper. How much paper will be required to do so ?

Answer

Length of the matchbox (l) = 4 cm, breadth (b) = 2.5 cm, height (h) = 1.5 cm
∴ Total surface area of the matchbox = 2 (lb + bh + lh)
= 2 (4 × 2.5 + 2.5 × 1.5 + 4 × 1.5)
= 2 (10 + 3.75 + 6)
= 2 × 19.75
= 39.5 sq. cm.
∴ 39.5 sq. cm paper will be required.

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Question 23 Marks

The length and the width of a mobile phone are 13 cm and 7 cm respectively. It has a screen PQRS as shown in the figure. What is the area of the screen ?

Answer

ABCD is the rectangle formed by the edges of the mobile. PQRS is the rectangle formed by leaving a 1.5 cm wide edge alongside AB, BC, and DC, and a 2 cm edge alongside DA.
Length of rectangle PQRS = 9.5 cm
Breadth of rectangle PQRS = 4 cm
Area of screen = Area of rectangle PQRS = 9.5 x 4
= 38 sq .cm

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Question 33 Marks

A rectangular playground is 65m long and 30m wide. A pathway of 1.5 m width goes all around the ground, outside it. Find the area of the pathway.

Answer

The playground is rectangular.
₹ABCD is the playground. Around it is a pathway 1.5 m wide.
Around ₹ABCD we get the rectangle ₹PQRS
Length of new rectangle PQRS = 65 + 1.5 + 1.5 = 68 m
Breadth of new rectangle PQRS = 30 + 1.5 + 1.5 = 33m
Area of path = Area of rectangle PQRS – Area of rectangle ABCD = 68 x 33 – 65 x 30
= 2244 – 1950
= 294 sq m

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Question 43 Marks

If the side of a square is tripled, how many times will its area be as compared to the area of the original square ?

Answer

Let the side of the square be a.
∴ Area of a square = (side)² = a²
New side of the square = 3 × a = 3a
∴ New area of the square = (3a)²
= 9a²
= 9 × area of original square
∴ If the side of a square is tripled, its area will become 9 times the area of the original square.

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Question 53 Marks

The area of a rectangle is 102 sq. cm. If its length is 17 cm, what is its perimeter ?

Answer

Area of a rectangle $=$ length $\times$ breadth
$
\begin{aligned}
& \therefore 102=17 \times \text { breadth } \\
& \therefore \text { breadth }=\frac{102}{17}=6 cm \\
& \text { Perimeter of rectangle }=2 \text { (length }+ \text { breadth) } \\
& =2(17+6) \\
& =2 \times 23 \\
& =46 cm
\end{aligned}
$
$\therefore$ The perimeter of rectangle is $46 cm$.

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Question 63 Marks

As shown in the figure, four napkins all of the same size were made from a square piece of cloth of length 1 m. What length of lace will be required to trim all four sides of all the napkins ?

Answer

Side of the square piece of cloth = 1 m
∴ Side of each napkin = 0.5 m
Length of lace that will be required for 1 napkin = perimeter of the napkin
= 4 x side = 4 x 0.5 = 2 m
∴ Perimeter of 4 napkins = 4 x 2 = 8 m
∴ 8 metre long lace will be required to trim all four napkins.

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Question 73 Marks

Given alongside is the diagram of a playground. It shows the length of its sides. Find the perimeter of the playground.

Answer

Side AF = side BC + side DE
∴ Side AF = 15 + 15 = 30 m
Side FE = side AB + side CD
∴ Side FE = 10 + 5 = 15 m
∴ Perimeter of the playground = side AB + side BC + side CD + side DE + side FE + side AF
= 10 + 15 + 5 + 15 + 15 + 30
= 90 m.
∴ The perimeter of the playground is 90 m.

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Question 83 Marks

If the side of a square is tripled, how many times the perimeter of the first square will that of the new square be ?

Answer

Let the length of the square be a.
Perimeter of square = 4 x side
= 4 x a = 4a
Side of new square = 3 x a = 3a
Perimeter of new square = 4 x side
= 4 x 3a = 3 x 4a = 3x perimeter of original square.
∴ The perimeter of new square will be three times the perimeter of original square.

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Question 93 Marks

If the length and breadth of a rectangle are doubled, how many times the perimeter of the old rectangle will that of the new rectangle be ?

Answer

Let the length of the old rectangle be l and breadth be b.
∴ Perimeter of old rectangle = 2(l + b)
Length of new rectangle = 2l and breadth = 2b
∴ Perimeter of new rectangle = 2(2l + 2b)
= 2 x 2 (l + b)
= 2 x perimeter of old rectangle
∴ The perimeter of new rectangle will be twice the perimeter of old rectangle.

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Maths 3 Mark Question

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