a prism and a pyramid have congruent triangle bases if their heights are both 15 meters what is the volume of each shape
To find the volume of a prism, multiply the area of the base by the height. Since the base of the prism and pyramid are congruent triangles, we can use the formula for the volume of a prism for both shapes.
For a prism:
Volume = base area x height
Volume = (1/2)bh x h
Volume = (1/2)(b x h) x h
Volume = (1/2)(base of triangle) x height x height
Volume = (1/2)(base of triangle) x (height)^2
For a pyramid:
Volume = (1/3) x base area x height
Volume = (1/3) x (1/2)(b x h) x h
Volume = (1/6)(b x h) x h
Volume = (1/6)(base of triangle) x (height)^2
Since the base of the triangle for both shapes is the same, and the height is given as 15 meters, the volume of each shape is:
Volume of prism = (1/2)(base of triangle) x (height)^2 = (1/2)(base of triangle) x 15^2 = (225)(base of triangle)
Volume of pyramid = (1/6)(base of triangle) x (height)^2 = (1/6)(base of triangle) x 15^2 = (225/6)(base of triangle)
Therefore, the volume of both the prism and pyramid is 225 times the area of their congruent triangle bases.