**VOLUME**

**Rectangular**

P

rism

P

rism

Mrs. Romig's Math Class

Students will be able to solve real world math problems involving area and volume of 2D and 3D objects

**Let's Review!**

What is a prism?

A polyhedron with two parallel, congruent bases.

What is the base of a rectangular prism?

Think carefully.

A triangle is the base! This prism has two congruent and parallel triangular faces.

What is the base of a rectangular prism?

It is a rectangle! This prism has two congruent and parallel rectangular faces.

What is the formula to find the area of a rectangle? A triangle?

A= l x w

**Triangular Prism**

**What**

**is**

**volu**

m

e

?

m

e

?

**8th Grade MATH**

To calculate volume...

V= B x h

To calculate volume, multiply the area of the base, B, by the height, h.

The volume, V, of a rectangular prism is the product of the length, l, the width, w, and the height. This is the area of the base (length x width= B), multiplied by the height.

KEY CONCEPT

V= B x h

Let's try a problem together!

Find the volume of the rectangular prism.

V= l x w x h

Volume of a prism

V= 5 x 4 x 3

l=5, w=4, h=3

V= 60

Multiply.

5cm

4cm

3cm

The volume is 60 cubic centimeters.

Now you try!

Find the volume of the prism.

9.5 m

5m

3m

V= ?

V= 142.5 cubic meters

Let's do a real world problem!

John has two lunch boxes. He wants to choose the one that let's him carry the most food because he is extra hungry today. His Superman lunch box has a length of 10in, a width of 3.75in, and a height if 7.5in. His Ohio State lunch box has a length of 9.5in, a width of 3.75in, and a height of 8in. Find the volume of the lunch boxes, and decide which one John should choose.

Since the Superman lunch box has a volume of 285 cubic inches and the Ohio State box's volume is 281.5 cubic inches, John should take the Superman lunch box!

Now, get with a buddy and calculate the volume of these following prisms. Remember, always label your answer!

Remember, V=B x h

The volume, V, of a triangular prism is the area of the base times the height.

But the base of a triangular prism is a triangle. So the area of the base equals

(b x h)/2

. *b=base of the triangle, and h=height of the triangle

Therefore, V=

((b x h)/2)) x h

=

B x h

Let's do a problem together!

Find the volume of the triangular prism.

The area of the triangle is (6 x 8)/2, so replace B with (6 x 8)/2.

V=

V= B x h Volume of a prism

V= ((6 x 8)/2) x h Replace B with ((6 x 8)) x h.

V=((6 x 8)) x 9 The height of the prism is 9.

V= 216 Multiply

6 ft

height of triangle

8 ft

9 ft

The volume is 216 cubic feet.

Now you

try...

Find the volume of the triangular prism.

4 in

7 in

5 ft

V= ?

V= 140 cubic feet

Real world problem?

What is the volume of this door wedge?

3 cm

7 cm

6 cm

V= 63 cubic centimeters

Now get with a friend and try these!

Circles

Rectangles

Perimeter - all the way around a figure

Area - the number of square units in a figure. A = L x W

Triangles

perimeter - add up all the sides

Area

Calculate the

area of this figure.

A = L x W

A = 4 x 2

A = 8 units squared

**Cylinder**

Finding the VOLUME of a Cylinder

Volume of a cylinder

is equal to the

area of the base x height

Your turn!

Find the volume of the cylinders below, using 3.14 for pi. Round answers to the nearest tenth. Be sure to label your answer using the correct units!

Check your answer!

Real World Example...

Did you get it right?