The volume of a Trapezoidal Prism and Cylinder?

Question

Hi. I need a solution to this problem. I am currently on the section in my maths book called Volume . There is a question and i do not know the answer. The shape is a Trapezoidal Prism, hence the title. There are four measurements: 7cm, 3cm, 9 cm and 4 cm. I have read the answer and it says that it is V=148.5 cm3. It's very strange because i know that the formula for a Trapezium is 1/2(a+b)x h, and there is 4 measurements. Also why is the answer in cubic centimetres. I need to know the steps on how to work it out etc.

Here is a picture of it: http://img208.imageshack.us/img208/4513/...

Also i need help on the volume of a Cylinder. The length is 1.1m and the constant area of cross section is 90cm. The answer is 0.70cm3. Could someone also explain steps on how to work it out. Also why is the answer in cubic centimetres?

Here is a picture of it: http://img62.imageshack.us/my.php?image=...
All comments are much appreciated. Thank You.

Answer 1

To get the volume of either the trapazoid or cylinder, you first need to find the area of the floor and then multiply that answer times the height.

Area of trapezoid is A=1/2h(B+b) (The two parallel lines are the bases.) Then multiply times the height of the trapezoid.

Area of circle is A=(pi)r^2. Then multiply times the height of the cylinder.

Answer 2

Trapezoidal Prism Problem Split the shape into two parts (1 cube with dimensions of 3cm x 9cm x 4cm and one prism with dimensions of 3cm x 3cm x 9cm). Volume of cube = l x w x h = 9cm x 4cm x 3cm = 108cm3 Volume of prism = 1/2(l x w x h) = 1/2((7cm - 4cm) x 9cm x 3cm = 40.5cm3 Sum both volumes = 108cm3 + 40.5cm3 = 148.5cm3 Cylinder Problem Volume of a cylinder = pi x r2 x h In the picture the diameter is 90 cm (what you refer to as constant are of cross section), this is really the longest length across the top of the cylinder. The formula asks for radius so divide by 2, therefore r = 45cm. The answer is in cubic cm, so we will transform h to cm, h = 110 cm. Now, we can solve the problem. V = pi x r2 x h V = 3.14 x 45cm^2 x 110cm V = 7.0 x 10^5 cm3 or 0.7m3 (This tells me the answer is actually in m3 not cm3) Since we know the relationship of radius to diameter we can substitute diameter into the volume formula and we could use all the number directly from the question. V = pi x (d^2)/4 x h V = 3.14 x (90^2)/4 x 110 V = 0.7m3

Answer 3

for the cylinder, by what you've given, the answer is wrong. it's 990 cubic centimeters.

The links you provided aren't working for me, so unless I know what the measurements are specifically, I can't help. I can only suggest that three of them are sides of the base, maybe.