Question

OXYZ is a pyramid whose base is a right-angled
triangle where XY = 7 m and YZ = 4 m. Given that
the height of the pyramid is 5 m, find its volume.​

Answer 1

Given:

• OXYZ is a pyramid whose base is a right-angled  triangle  where XY = 7m and YZ = 4m
• Height of the pyramid is 5 m.

To Find:

• Find volume of pyramid.

Solution:

Volume of a pyramid is given by

                      $V =\frac{base area \times height}{3}$

The base of the pyramid is triangle

Since angle xyz is 90 degree, xy is base and yz is height of the base triangle.

  Therefore base area       $= \frac{xy \times yz }{2}$

                                         $= \frac{ 7 \times 4}{2} \\\\=14m^2$

Volume of the pyramid   $(V)$ $= \frac{14 \times 5}{3}$

                                 $(V) = \frac{70}{3} m^3$

Thus, The volume of pyramid is $(V) = \frac{70}{3} m^3$