A right wedge is a wedge with parallel side triangles. It have two side bases a and b, top edges e and height h. The task is to find the volume of the given rectangular right wedges.
Examples:
Input: a = 2, b = 5, e = 5, h = 6
Output: Volume = 45.0
Input: a = 5, b = 4, e = 4, h = 6
Output: Volume = 56.0
Approach:
Va is the volume of triangular pyramid i.e. Va = (1 / 3) * area of triangle * (e – a)
Area of triangle = (1 / 2) * b * h
i.e Va = ( 1 / 3 ) * (( 1 / 2 ) * ( b * h * (e – a)))
Vb is a volume of triangular prism i.e. Vb = area of cross section * length(side)
i.e. Vb = (1 / 2) * (b * h * a)
Total Volume = Va + Vb
= (1 / 3) * ((1 / 2) * (b * h * ( e – a ))) + (1 / 2) * (b * h * a)
= (1 / 6) * (b * h * (e – a)) + (1 / 2) * (b * h * a)
= ((b * h) * (e – a) + 3 * b * h * a) / 6
= (b * h * e – b * h * a + 3 * b * h * a) / 6
= (b * h * e + 2 * b * h * a) / 6
= (b * h / 6) * (2 * a + e)
Volume of the rectangular right wedge = (b * h / 6) * (2 * a + e) where a and b are the side bases, e is the top edge and h is the height of the rectangular right wedge.
Below is the implementation of the above approach:
C++
// CPP program to find volume of rectangular right wedge #include <bits/stdc++.h> using namespace std; // function to return volume//of rectangular right wedgedouble volumeRec(double a,double b,double e,double h){ return (((b * h )/ 6)*(2 * a + e));} // Driver code int main() { double a = 2; double b = 5; double e = 5; double h = 6; printf("Volume = %.1f",volumeRec(a, b, e, h)); return 0; }// This code contributed by nidhiva |
Java
// Java implementation of the approachclass GFG { // Function to return the volume // of the rectangular right wedge static double volumeRec(double a, double b, double e, double h) { return (((b * h) / 6) * (2 * a + e)); } // Driver code public static void main(String[] args) throws java.lang.Exception { double a = 2, b = 5, e = 5, h = 6; System.out.print("Volume = " + volumeRec(a, b, e, h)); }} |
Python3
# Python3 implementation of the approach # Function to return the volume # of the rectangular right wedge def volumeRec(a, b, e, h) : return (((b * h) / 6) * (2 * a + e)); # Driver code if __name__ == "__main__" : a = 2; b = 5; e = 5; h = 6; print("Volume = ",volumeRec(a, b, e, h)); # This code is contributed by AnkitRai01 |
C#
// C# implementation of the approachusing System;class GFG { // Function to return the volume // of the rectangular right wedge static double volumeRec(double a, double b, double e, double h) { return (((b * h) / 6) * (2 * a + e)); } // Driver code public static void Main() { double a = 2, b = 5, e = 5, h = 6; Console.WriteLine("Volume = " + volumeRec(a, b, e, h)); }}// This code is contributed by vt_m. |
Javascript
<script>// javascript program to find volume of rectangular right wedge // function to return volume//of rectangular right wedgefunction volumeRec( a, b, e, h){ return (((b * h )/ 6)*(2 * a + e));} // Driver code let a = 2; let b = 5; let e = 5; let h = 6; document.write("Volume = "+volumeRec(a, b, e, h).toFixed(1)); // This code is contributed by Rajput-Ji </script> |
Volume = 45.0
Time Complexity: O(1)
Auxiliary Space: O(1)
Ready to dive in? Explore our Free Demo Content and join our DSA course, trusted by over 100,000 neveropen!
