Question

*How much does it cost to paint a cuboidal wooden box of 2 m length, 1 m width and 1 m height at the rate of Rs 40 per sqm.?*

1️⃣ Rs 400
2️⃣ Rs 800
3️⃣ Rs 240
4️⃣ Rs 480​

Answer 1

Solution :

Given,

$\text {Dimensions of the Cuboidal Box} = \begin {cases} \begin {aligned} Length &= 2m\\Breadth &= 1m\\Height &= 1m \end{aligned} \end {cases}$

$\begin {aligned} \therefore\ \text{Total Surface Area of the Box} &= \mathtt {2 (lb + bh + hl)\ sq.\: units}\\\\&\Rightarrow 2 (2 \times 1 + 1 \times 1 + 1 \times 2)\ m^2\\\\&= 2 (2 + 1 + 2)\ m^2 \implies (2 \times 5)\ m^2\\\\&= \bf 10\ m^2 \end{aligned}$

$\begin{gathered} \end{gathered}$

∴ Area of the Cuboidal Wooden Box = 10 m²

$\begin{gathered} \end{gathered}$

Cost of Painting the Box/ m² = Rs. 40

∴ Total Cost of Painting the Box = $Rs.\ (10\ m^2 \times 40) = \bf Rs.\ 400$

$\begin{gathered} \end{gathered}$

Hence, the Cost of Painting the Cuboidal Wooden Box is Rs. 400

Option A is the Right Answer...

Additional Information :

Cuboid :-

A Solid bounded by Six Rectangular faces, 12 Edges and 8 Vertices.

E.g. A Rectangular Room is in the form of a Cuboid and its Four Walls are its Lateral Faces.

$\begin {gathered} \end {gathered}$

FORMULAE :-

Consider a Cuboid of Length = l units, Breadth = b units and Height = h units.

Then, we have -

(i) Volume of the Cuboid = $\mathtt{(l \times b \times h)\ cu.\: units}$

(ii) Diagonal of the Cuboid = $\mathtt{\sqrt {l^2 + b^2 + h^2}\ units}$

(iii) Lateral Surface Area of the Cuboid = $\mathtt{[2h \times (l + b)]\ sq.\: units}$