Exercises on Mensuration: With Solutions, Forming Key to Chamber's 'Mensuration'. |
Common terms and phrases
1st point 8th square 9 inches angle equal angle or oblong circumference circumscribing circle cone Curved line bending cylinder diagonal diameter Draw a Horizontal draw a Slanting draw an Upright draw another Horizontal equal parts taken equilateral triangle feet 6 inches fifth find the area form a rectangle fourth frustum half a tenth half circle height is equal Horizontal line equal Horizontal Straight line horizontally bear inscribed circle lateral surface left upright side lesser squares taken line are equal line forms line is divided nine perimeter point draw point of division Q-Draw Q-How many lesser Q-Into Q-Join Q-What proportion Q-Which is greatest Q.-Have radii rect rectangle equal rectangle whose height rectangles taken right upright side seventh sixth slant height Slanting line slants upwards sphere square divided square inches taken together horizontally total surface upper extremity upright line Upright Straight lines whole square
Popular passages
Page 134 - ... by equal regular polygons of either three, four, or six sides. 262. A plane surface may be entirely covered by a combination of squares and regular octagons having the same side, or by dodecagons and equilateral triangles having the same side.
Page 136 - From this it readily follows that all the three lines drawn from the angles of a triangle to the middle of the opposite sides, pass through one and the same point.
Page 137 - The area of a regular inscribed hexagon is a mean proportional between the areas of the inscribed and circumscribed equilateral triangles.
Page 108 - ... respectively, on a side and the volume of a prism of the same altitude whose base is a section of the frustum parallel to its bases and equidistant from them.
Page 68 - Find the area of a sector of a circle whose radius is 21 feet, the length of the arc being 15 feet.
Page 132 - Prove that the area of the regular hexagon inscribed in a circle is twice the area of the inscribed equilateral triangle. Verify this fact by cutting a regular hexagon out of paper, and folding it. Ex. 1195. The side of an equilateral triangle circumscribed about a circle is twice the side of an inscribed equilateral triangle.
Page 134 - A = the side of the similar circumscribed polygon, then, 2aR 2AR -a-) V(4R 3 +A 3 ) 272. If o = the side of a regular polygon inscribed in a circle whose radius is R,, and a...
Page 114 - Find the radius of a sphere which has the same volume as a cone whose height = h, and radius of base 6.
Page 63 - Show that the areas of similar triangles are to each other as the squares of the homologous sides.