Name: Flat & Curved Surfaces
Uploaded: 2019-07-19
Duration: 4 min 21 s
Description: Let's identify different surfaces of objects and how these surfaces play a hand in deciding if the object will roll, slide or stack on top of each other. Let...

Question

A water trough in the shape of a prism has trapezoidal faces. The dimensions of a base are shown in this picture:

The length of the trough is 80 centimeters. It is to be painted inside and outside. How much would be the cost at 100 rupees per square metre?

Accepted Answer

As, we can see the figure is of trapezoidal shape,

Now we add the area of two edge faces and three lateral faces one on bottom and another on sides.

In figure, $AB = 50 cm, CD = 70 cm$

$EC = \frac{70 - 50}{2} = 10 cm BE = 24 cm {BC}^{2} = {BE}^{2} + {EC}^{2} = 24^{2} + 10^{2} {BC}^{2} = 576 + 100 = 676 BC = \sqrt 676 = 26 cm$

Area of the trapezoidal faces of the water $= \frac{1}{2} h (a + b)$

$\Rightarrow \frac{1}{2} \times 24 \times (70 + 50)$

$= 12 \times 120 = 1440 {cm}^{2}$

Area of two trapezoidal faces $= 2 \times 1440 = 2880 {cm}^{2}$

Area of two rectangular faces on sides $= 2 \times 80 \times 26 = 4160 {cm}^{2}$

Area of rectangular face at bottom $= 50 \times 80 = 4000 {cm}^{2}$

Total Area $= 2880 + 4160 + 4000 = 11040 {cm}^{2} = 1.1 m^{2}$

Total area to be painted $= 2 \times 1.1 = 2.2 m^{2}$

Total cost $= 2.2 \times 100 = 220 = ₹ 220$

Hence, the required answer is $₹ 220$ .

A water trough in the shape of a prism has trapezoidal faces. The dimensions of a base are shown in this picture:

The length of the trough is 80 centimeters. It is to be painted inside and outside. How much would be the cost at 100 rupees per square metre?

Important Questions on Prisms

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