A low land, 48m long and 31.5 m broad is raised to 6.5 dm. For this, earth is removed from a cuboidal hole, 27 m long and 18.2 m broad, dug by the side of the land. The depth of the hole will be?
A man rows 12 km in 5 hrs against
the stream, the speed of current being 4 kmph. What time will be taken by him to row 15 km with the stream?
The length of two parallel chords of a circle of radius 5 cm are 6 cm and 8 cm in the same side of the centre. The distance between them is?
Pls help***
If the depth is x dm, then we have
48*31.5*6.5 = 27*18.2*x
If his speed is x in still water then
12/(x-4) = 5
Use that x to evaluate
15/(x+4)
Draw a diagram. If you draw a radius perpendicular to the chords, you bisect them. You then have two 3-4-5 triangles (the radius of 5 is the hypotenuse)
So, now it's easy to see how far apart they are.
To answer the given questions, we will go step by step and explain the process to find the solution.
1. Finding the depth of the hole:
Given:
Low land dimensions: Length = 48m, Breadth = 31.5m, Height increased = 6.5dm (which is 0.65m)
To find the depth of the hole, we need to subtract the increased height of the land from the height of the cuboidal hole.
Height of the hole can be found by subtracting the increased height of the land from the height of the cuboidal hole:
Depth of the hole = Height of the cuboidal hole - Increased height of the land
Given:
Length of the hole = 27m
Breadth of the hole = 18.2m
The formula to calculate the volume of a cuboid is:
Volume = Length × Breadth × Height
Given that both the land and the hole have the same area, we can equate their volumes:
48 × 31.5 × 0.65 = 27 × 18.2 × Height of the hole
From the equation, we can find the value of Height of the hole.
2. Finding the time taken to row 15km with the stream:
Given:
Distance to row with the stream = 15km
Speed of the stream = 4km/h
To find the time taken to row 15km with the stream, we will calculate the effective speed of the boat.
Speed of the boat with the stream = Speed of rowing + Speed of the stream
Speed of the boat against the stream = Speed of rowing - Speed of the stream
Given:
Distance to row against the stream = 12km
Time taken to row against the stream = 5 hours
To calculate the speed of rowing, we will use the formula:
Speed = Distance / Time
From the given information, calculate the speed of rowing and then calculate the speed of the boat with the stream.
Now, using the formula of speed, calculate the time taken to row 15km with the stream.
3. Finding the distance between two parallel chords of a circle:
Given:
Radius of the circle = 5cm
Chord 1 length = 6cm
Chord 2 length = 8cm
The distance between two parallel chords can be calculated using the radius and the lengths of the chords.
First, consider the two chords as the bases of two right-angled triangles, with the hypotenuse being the radius of the circle.
Now, for both triangles, calculate the height from the center of the circle to the chord (which is half the length of the chord).
The distance between the two chords is twice the difference between their heights.
By applying the Pythagorean theorem and solving the equations, calculate the heights and then the distance between the two chords.
By following these steps, you should be able to find the solutions to the given questions.