You’ll find the volume by multiplying the area of the base $B$ with the height $h$:

Volume

The formula for the volume of a cylinder is $V=B\cdot h$. You have the height $h$, but have to find the base area $B$. Since the base area in a cylinder is a circle, you’ll have to find the area of a circle:

Now you’ll find the volume of a cylinder by multiplying the base area $B$ with the height $h$:

Surface Area

To find the surface area of a cylinder, you add together the areas of all the sides. The green rectangle you see on the drawing comes from cutting and folding out the walls of the cylinder. First, you calculate the area of the top and bottom of the cylinder (they have the same area), and then the area of the rectangle which is the height. The length of the rectangle is the circumference of the circle (see the figure): $$\begin{array}{llll}\hfill \text{Area of a circle}& =\pi r^2& \hfill & \\ \hfill & =\pi \cdot 2.0\text{cm}\cdot 2.0\text{cm}& \hfill & \\ \hfill & \approx 12.6{\text{cm}}^2,& \hfill & \\ \hfill \text{Area of a rectangle}& =l\cdot h& \hfill & \\ \hfill & =2\pi r\cdot h& \hfill & \\ \hfill & =2\cdot \pi \cdot 2.0\text{cm}\cdot 8.0\text{cm}& \hfill & \\ \hfill & \approx 101{\text{cm}}^2.& \hfill & \end{array}$$

The surface area of a cylinder then becomes

You’ll find the volume of the pyramid by multiplying the area of the base area $B$ with the height $h$, and the dividing by 3:

Volume

The volume has the formula $V=B\cdot h$, so you first need to find the area of the base $B$. The area of the circle is:

Then you’ll find the volume of the cone by multiplying the area of the base $B$ with the height $h$, and then divide by 3: $$\begin{array}{llll}\hfill \text{Volume}& =\frac{B\cdot h}{3}& \hfill & \\ \hfill & =\frac{28.3{\text{cm}}^2\cdot 7.0\text{cm}}{3}& \hfill & \\ \hfill & \approx 66.0{\text{cm}}^3.& \hfill & \end{array}$$

Surface Area

You’ll find the surface area by using the formula for the surface area of a cone. Here you can put your values directly in to the formula and calculate.

Volume

You1’ll find the volume by using the formula for the volume of a sphere: $$\begin{array}{llll}\hfill \text{Volume}& =\frac{4\pi r^3}{3}& \hfill & \\ \hfill & =\frac{4\cdot \pi \cdot 5.0\text{cm}\cdot 5.0\text{cm}\cdot 5.0\text{cm}}{3}& \hfill & \\ \hfill & \approx 524{\text{cm}}^3.& \hfill & \end{array}$$

Surface Area

You’ll find the surface area by using the formula for the surface area of a sphere: $$\begin{array}{llll}\hfill \text{Surface area}& =4\pi r^2& \hfill & \\ \hfill & =4\cdot \pi \cdot 5.0\text{cm}\cdot 5.0\text{cm}& \hfill & \\ \hfill & \approx 314{\text{cm}}^2.& \hfill & \end{array}$$