Question

I need help with these shapes. Cube Dimensions:Length: 11 cmWidth: 11 cmHeight: 11 cmCone Dimensions: height: 9 cmslant height: 11 cmradius: 4 cm

Answer 1

Cube:

The base area of a cube is the area of any of the faces, this is because all the faces of the cube have the same area.

The area of one face of the cube is the product of two of its edge lengths:

`\begin{gathered} BA=s^2 \\ BA=11cm\cdot11cm \\ BA=121cm^2 \end{gathered}`

The base area of the cube is 121cm^2.

The surface area is the sum of the areas of the faces of the cube. We already know the area of one of the faces, and that all the faces have the same area, which means that the surface area is 6 times the base area:

`\begin{gathered} SA=6\cdot BA \\ SA=6\cdot121cm^2 \\ SA=726cm^2 \end{gathered}`

The surface area of the cube is 726cm^2.

Cone:

The base area of the cone is the area of the circle that is in the base of it. To find it we can use the following formula:

`BA=\pi r^2`

Where r is the radius of the circle:

`\begin{gathered} BA=\pi(4cm)^2 \\ BA=16\pi cm^2 \end{gathered}`

The base area of the cone is 16πcm^2

The surface area of the cone is found using the following formula:

`SA=\pi rs+BA`

Where r is the radius, s is the slant height and BA is the base area:

`\begin{gathered} SA=\pi(4cm)(11cm)+16\pi cm^2 \\ SA=44\pi cm^2+16\pi cm^2 \\ SA=60\pi cm^2 \end{gathered}`

The surface area of the cone is 60πcm^2.