Mathematics: What is the volume of the composite figure? 715 units 2,035 units 2,750 units 3,465 units

Sum and difference problem.Larger number = (sum+difference)/2=(31+7)/2=19Smaller number = (sum-difference)/2=(31-7)/2=12...

What is the volume of the composite figure? 715

chayaharroch03

24.01.2022

Given:

Given that the composite figure is made up of a triangular prism and a pyramid.

The height of the pyramid is 19.5 units.

The length of the prism is 25 units.

The base of the triangle is 22 units.

The height of the triangle is 10 units.

We need to determine the volume of the composite figure.

Volume of the triangular pyramid:

The volume of the triangular pyramid can be determined using the formula,

$V=\frac{1}{3}(\frac{1}{2}bh)H_1$

where b is the base of the triangle and h is the height of the triangle and H₁ is the height of the pyramid.

Substituting b = 22 , h = 10 and H₁ = 19.5, we get;

$V=\frac{1}{3}(\frac{1}{2}(22)(10))(19.5)$

Simplifying, we get;

$V=\frac{1}{3}(\frac{1}{2}(220))(19.5)$

$V=\frac{1}{3}(110)(19.5)$

V=715

Thus, the volume of the triangular pyramid is 715 cubic units.

Volume of the triangular prism:

The volume of the triangular prism can be determined using the formula,

$V=\frac{lbh}{2}$

Substituting l = 25, b = 22 and h = 10, we get;

$V=\frac{25 \times 22 \times 10 }{2}$

$V=\frac{5500}{2}$

V=2750

Thus, the volume of the triangular prism is 2750 cubic units.

Volume of the composite figure:

The volume of the composite figure can be determined by adding the volume of triangular prism and triangular pyramid.

Thus, we have;

Volume = Volume of prism + Volume of pyramid.

Substituting the values, we have;

Volume = 2750+715=3465

Thus, the volume of the composite figure is 3465 cubic units.

Hence, Option d is the correct answer.

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