Mathematics, 23.05.2020 05:04 yfnal3x

Colton has a stone paperweight composed of a triangular pyramid on top of a triangular prism with the dimensions shown below. Use the drop-down menus to explain how to determine the volume of the paperweight. Need major help please

Colton has a stone paperweight composed of a triangular pyramid on top of a triangular prism with th

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Answer from: reganjones89

The complete statements are:

The area of the base of the prism is equal to the area of the base of the pyramid which can be determined by multiplying half the base and the heightTo find the volume of the triangular prism, multiply the area of the base by 4To find the volume of the triangular pyramid, multiply the area of the base by 1/3 of 7The volume of the paperweight is approximately 79.17 cubic inches

Start by calculating the area of the base of the pyramid using:

$A_1 = \frac 12 \times base \times height$

So, we have:

$A_1 = \frac 12 \times 5 \times 5$

A_1 = 12.5

The volume of the triangular prism is then calculated using:

$V_1 = A_1 \times h$ --- i.e. the product of area and height (4)

So, we have:

$V_1 = 12.5 \times 4$

V_1 = 50

The volume of the triangular pyramid is then calculated using:

$V_2 = \frac 13 \times A_1 \times h_2$ --- i.e. the product of 1/3 of the area and height (7)

So, we have:

$V_2 = \frac 13 \times 12.5 \times 7$

V_2 = 29.17

The total volume of the shape is then as:

V = V_1 + V_2

V = 50 + 29.17

V = 79.17

Hence, the volume of the paperweight is approximately 79.17 cubic inches

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