Question

The composite figure is made up of a triangular prism and a pyramid. The two solids have congruent bases.

Answer 1

the correct question is
The composite figure is made up of a triangular prism and a pyramid. The two solids have congruent bases. What is the volume of the composite figure?

the complete question in the attached figure

we know that

[volume of a cone]=[area of the base]*h/3
[area of the base]=22*10/2-------> 110 units²
h=19.5 units
[volume of a cone]=[110]*19.5/3------> 715 units³

[volume of a triangular prism]=[area of the base]*h
[area of the base]=110 units²
h=25 units
[volume of a a triangular prism]=[110]*25------------> 2750 units³

[volume of a the composite figure]=[volume of a cone]+[volume of a a triangular prism]

[volume of a the composite figure]=[715]+[2750]-------> 3465 units³

the answer is
The volume of a the composite figure is 3465 units³

Answer 2

The volume of a composite figure which is made up of a triangular prism and a pyramid and these two solids have congruent bases is 3465 unit³.

How to find the volume of the composite figures?

To find the volume of the composite figures,

• Separate the figure.
• Calculate the volume of each figure by which the composite figure is made of.
• Add the volume of all the individual figures to get the total volume of composite figures.

The composite figure is made up of a triangular prism and a pyramid. The two solids have congruent bases.

The volume of the triangular pyramid figure is,

$V_t=\dfrac{1}{3}\times\dfrac{bh}{2}\times H$

Here, b is the base of the triangle, h is the height of the triangle and H is the height of the pyramid. Put the values,

$V_t=\dfrac{1}{3}\times\dfrac{22\times10}{2}\times 19.5\\V_t=715\rm\; unit^3$

The volume of the triangular prism figure is,

$V_p=\dfrac{lbh}{2}$

Here, l is the length of the prism. Put the values,

$V_p=\dfrac{25\times22\times10}{2}\\V_p=2750\rm\; unit^3$

Thus, the volume of the composite figure,

$V=715+2750\\V=3465\rm\; unit^3$

Thus, the volume of a composite figure which is made up of a triangular prism and a pyramid and these two solids have congruent bases is 3465 unit³.

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