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?

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 = 70 – 50 2 = 10 cm BE = 24 cm BC 2 = BE 2 + EC 2 = 24 2 + 10 2 BC 2 = 576 + 100 = 676 BC = √ 676 = 26 cm Area of the trapezoidal faces of the water = 1 2 h a + b ⇒ 1 2 × 24 × 70 + 50 = 12 × 120 = 1440 cm 2 Area of two trapezoidal faces = 2 × 1440 = 2880 cm 2 Area of two rectangular faces on sides = 2 × 80 × 26 = 4160 cm 2 Area of rectangular face at bottom = 50 × 80 = 4000 cm 2 Total Area = 2880 + 4160 + 4000 = 11040 cm 2 = 1 . 1 m 2 Total area to be painted = 2 × 1 . 1 = 2 . 2 m 2 Total cost = 2 . 2 × 100 = 220 = ₹ 220 Hence, the required answer is ₹ 220 .

E M B I B E

Standard 9 Mathematics Part - 2>Chapter 4 - Prisms>Exercise 2

Kerala Board Solutions for Chapter: Prisms, Exercise 2: Exercise 2

Author:Kerala Board

Kerala Board Mathematics Solutions for Exercise - Kerala Board Solutions for Chapter: Prisms, Exercise 2: Exercise 2

Attempt the free practice questions on Chapter 4: Prisms, Exercise 2: Exercise 2 with hints and solutions to strengthen your understanding. Standard 9 Mathematics Part - 2 solutions are prepared by Experienced Embibe Experts.

Questions from Kerala Board Solutions for Chapter: Prisms, Exercise 2: Exercise 2 with Hints & Solutions

HARD

9th Kerala Board

IMPORTANT

Standard 9 Mathematics Part - 2>Chapter 4 - Prisms>Exercise 2>Q (1)

The base of a prism is an equilateral triangle of perimeter $12$ centimetres and its height is $5$ centimetres. What is its total surface area?

HARD

9th Kerala Board

IMPORTANT

Standard 9 Mathematics Part - 2>Chapter 4 - Prisms>Exercise 2>Q (2)

Two identical prisms with right triangles as base are joined to form a rectangular prism as shown below:

Question Image

What is total surface area?

HARD

9th Kerala Board

IMPORTANT

Standard 9 Mathematics Part - 2>Chapter 4 - Prisms>Exercise 2>Q (3)

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

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