5 Mark Question

Question 15 Marks

An open box of length 1.5 m, breadth 1 m, and height 1 m is to be made for use on a trolley for carrying garden waste. How much sheet metal will be required to make this box? The inside and outside surface of the box is to be painted with rust proof paint. At a rate of Rs 150 per sq. m, how much will it cost to paint the box ?

Answer

Length of the box (l) = 1.5 m, breadth (b) = 1 m, height (h) = 1 m
Since, the box is open at top,
∴ Sheet required to make the box = total surface area of the box – area of the top
= 2 (lb + bh + lh) – lb
= 2lb + 2bh + 2lh – lb
= lb + 2bh + 2lh
= 1.5 × 1 + 2 × 1 × 1 + 2 × 1.5 × 1
= 1.5 + 2 + 3
= 6.5 sq. m.
Since, the inside and outside surface of the box are to be painted.
∴ Area to be painted = 2 × Area of the box = 2 × 6.5 = 13 sq. m.
Total cost of painting = area to be painted × rate per sq. m.
= 13 × 150
= Rs 1950
∴ 6.5 sq. m. sheet of metal will be required and the cost of painting the box will be Rs 1950.

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Question 25 Marks

A rectangular hall is 12 m long and 6 m broad. Its flooring is to be made of square tiles of side 30 cm. How many tiles will fit in the entire hall? How many would be required if tiles of side 15 cm were used ?

Answer

Area of the rectangular hall = length $\times$ breadth
$
\begin{aligned}
& =12 \times 6 \\
& =72 \text { sq. } m \text {. }
\end{aligned}
$
Side of the square shaped tile $=30 cm$
$
\begin{aligned}
& =\frac{30}{100} m \ldots\left[1 cm =\frac{1}{100} m \right] \\
& =\frac{3}{10} m
\end{aligned}
$
Area of the tile $=(\text { side })^2$
$
\begin{aligned}
& =\left(\frac{3}{10}\right)^2 \\
& =\frac{9}{100} sq \cdot m
\end{aligned}
$
Number of tiles required $=\frac{\text { Area of the hall }}{\text { Area of each tile }}$
$=72 \div \frac{9}{100}$
$=72 \times \frac{100}{9}$
$=800$
$\therefore 800$ square shaped tiles of $30 cm$ side will be required.
If the side of the square is reduced to half, its area will become $\frac{1}{4}$ times the original.
i. e. number of tiles required will become 4 times the original tiles.
$\therefore$ Number of tiles required $=4 \times$ number of tiles of side $30 cm$
$=4 \times 800$
$=3200$
$\therefore 3200$ square shaped tiles of $15 cm$ side will be required.

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Question 35 Marks

Is there another way to find the area of the pathway in the problem above ?

Answer

Yes. The area of the pathway can be found by dividing it into rectangles and adding the areas of these rectangles.
Length of rectangle 1 = 30 + 1.5 + 1.5 = 33 m
Breadth of rectangle 1 = 1.5 m
∴ Area of rectangle 1 = 33 x 1.5
= 49.5 sq. m
Area of rectangle 4 = Area of rectangle 1
= 49.5 sq. m.
Length of rectangle 2 = 65 m
breadth of rectangle 2 = 1.5 m
∴ Area of rectangle 2 = 65 x 1.5
= 97.5 sq. m.
Area of rectangle 3 = area of rectangle 2
= 97.5 sq. m.
∴ Area of pathway = Sum of area of the 4 rectangles = 49.5 + 49.5 + 97.5 + 97.5
= 294 sq. m.

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Maths 5 Mark Question

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