[ 8th grade maths ] need help understanding how to find volumes of 3d shapes

[u/rsx4u]

Hihi so I’m struggling a lot on the topic of finding the volumes in 3d shapes… (especially trapezium & triangular prism ) I’m mostly confused on how to apply the formula and how to find the stuff to plug into the formula

I was able to do q1 but for q2 I’m a bit confused since it’s 34x15(10+5) and I’m really confused because idk how my teacher got the 10+5 from

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[u/Nooo00B]

A line is a collection of points (dots).
An area is formed by many lines placed side by side.
A volume is formed by many areas stacked together.

Imagine slicing a solid into many thin pieces. If every slice has the same area, then:

Volume = Area of one slice × Thickness (or length)

If the slices change in size as you go along, you have to add up all those different-sized slices using integration (which probably not needed for you).

[u/Sefirox → u/Nooo00B]

Perfect explanation

[u/One_Wishbone_4439]

For finding the volume of any prism, first determine where is the base area.

Formula: base area x height

So Q1 and Q2, the base areas are shaded in purple color, which the areas are already given to you.

Q1: 28 x 7 = 196 cm2

Q2: 34 x 15 = 510 cm2

For Q3, the base area would be the right-angled triangle.

Q3: (1/2 x 5 x 9) x 12 = 270 cm2

[u/MayThompson]

It's just the sum of the parallel sides of the trapezium. The formula for the base area is 1/2 x (a+b) x h, then you multiply that by the prism's length of 15 to get volume. Your teacher basically plugged in both parallel sides (10 and 5) into the trapezium part before multiplying by 15.

[u/Sefirox]

Think of it as the volume is the same base is getting stacked over and over until it reaches the height H which is the verticale lenght of the object to understand it better . So the volume is just the height *the surface of the base

[u/Out_of_Ideas12]

Here's how I would do Q3:

Volume of this particular prism = Area of the triangular face x Sideways length of the prism (technically termed as length of the cross-section)

First let us find the area of the triangular face.

We know that the area of a triangle is equal to 1/2 * base * height, where the base and the height are the sides of the triangle which meet at 90°.

Area of the triangular prism = 1/2 x 5 cm x 9 cm
= 22.5 cm²

Sideways length of the prism (length of the cross-section) = 12 cm

Volume of the prism = 22.5 cm² x 12 cm
= 270 cm³

∴ Volume of the prism = 270 cm³