A Practical Application of the Principles of Geometry to the Mensuration of Supe
A Practical Application of the Principles of Geometry to the Mensuration of Supe
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Cor.
62 MENSURATION OF THE CONE.
2. If the axis of an oblique cone be 738, and make an angle of 30° with the plane of the base ; and if the circum- ference of the base be 355, what is the solidity ?
Ans. 1233536.
Problem V.. To find the convex surface of a frustum of a right cone. 67. Multiply half the slant-height by the sum of THE peripheries OF THE TWO ENDS.
This is the rule for a frustum of a pyramid ; (Art. 51. ) and is equally applicable to a frustum of a cone, if a cone be considered as ...a pyramid of an infinite number of sides. (Art. 63. ) Or thus, Let the sector ABV represent the convex surface of a right cone, (Art. 65. ) andyDCV the surface of a portion of the cone, cat off by a plane parallel to the base. Then will ABCD be tbe surface of the frustum.
Let AB=a, DC=6, YI>=d, AD=h. '^ Then the area ABV =iaX{h-\-d)=iah+iad. (Art. 34. ) And the area 'DCY=^bd. Subtracting the one from the other.
The area ABDC=iaA+iac/ — ^bd.
But d : d-\-h :\h : a. (Sup. Euc. 8. 1. )* Therefore ^ad^ ibd=ibh.
What to read after A Practical Application of the Principles of Geometry to the Mensuration of Supe?
You can find similar books in the "Read Also" column, or choose other free books by Jeremiah Day to read onlineMoreLess
To quickly assess the difficulty of the text, read a short excerpt:
Cor.
62 MENSURATION OF THE CONE.
2. If the axis of an oblique cone be 738, and make an angle of 30° with the plane of the base ; and if the circum- ference of the base be 355, what is the solidity ?
Ans. 1233536.
Problem V.. To find the convex surface of a frustum of a right cone. 67. Multiply half the slant-height by the sum of THE peripheries OF THE TWO ENDS.
This is the rule for a frustum of a pyramid ; (Art. 51. ) and is equally applicable to a frustum of a cone, if a cone be considered as ...a pyramid of an infinite number of sides. (Art. 63. ) Or thus, Let the sector ABV represent the convex surface of a right cone, (Art. 65. ) andyDCV the surface of a portion of the cone, cat off by a plane parallel to the base. Then will ABCD be tbe surface of the frustum.
Let AB=a, DC=6, YI>=d, AD=h. '^ Then the area ABV =iaX{h-\-d)=iah+iad. (Art. 34. ) And the area 'DCY=^bd. Subtracting the one from the other.
The area ABDC=iaA+iac/ — ^bd.
But d : d-\-h :\h : a. (Sup. Euc. 8. 1. )* Therefore ^ad^ ibd=ibh.
What to read after A Practical Application of the Principles of Geometry to the Mensuration of Supe?
You can find similar books in the "Read Also" column, or choose other free books by Jeremiah Day to read onlineMoreLess
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