Question

What’s the volume and surface area of the object shown ?

Answer 1

Volume of object = 42 cubic cm

Surface area of object = 96 square cm

Explanations:

The given figure is a triangular prism.The formula for calculating its volume is expressed as:

`volume\text{ }of\text{ prism}=BH`

where:

B is the base area

H is the height of prism

`\begin{gathered} volume\text{ of }prism=((1)/(2)*4*3)*7 \\ volume\text{ of }prism=6*7 \\ volume\text{ of }prism=42cm^3 \end{gathered}`

Determine the surface area of the prism

The surface area if the sum of all the faces of the prism.The faces consists of 3 rectangles and 2 triangles. The surface area is calculated as:

`\begin{gathered} Surface\text{ area}=2(0.5*3*4)+(7*4)+(3*7)+(5*7) \\ Surface\text{ area}=12cm^2+28cm^2+21cm^2+35cm^2 \\ Surface\text{ area}=96cm^2 \end{gathered}`

Hence the surface area of the object shown is 96 square cm