Question

5 cm3 cm3 cm5 cm3 cmPrisma5 cmPrism BWhich of the following statements are true about the solids shown above?Check all that apply.A. Prisms A and B have different values for lateral surface area.O B. Prism B has a total surface area of 110 cm?O C. Prism A has a lateral surface area of 60 cm?D D. Prism B has a larger surface area.

Answer 1

Note that the lateral surface area is the area of the faces of the solid, excluding the cross-sectional faces i.e. faces which are perpendicular to the longitudinal axis.

The lateral surface area of prism A is calculated as,

`\begin{gathered} LSA_A=2(5*3)+2(5*3)_{} \\ LSA_A=30+30 \\ LSA_A=60 \end{gathered}`

Similarly, the lateral surface area of prism A is calculated as,

`\begin{gathered} LSA_B=2(3*5)+2(5*5)_{} \\ LSA_B=30+50 \\ LSA_B=80 \end{gathered}`

Clearly, prisms A and B have different values of lateral surface area.

So option A is the correct statement.

The total surface area is the sum of all the faces of the solid.

Since we have already calculated the LSA i.e. sum of area of 4 faces of the prism, we can add the area of the two remaining cross sectional faces to get the total area.

The total cross section area of prism B is calculated as,

`\begin{gathered} A_B=2(5*3) \\ A_B=30 \end{gathered}`

So the total surface area of prism B becomes,

`\begin{gathered} TSA_B=LSA_B+A_B_{} \\ TSA_B=80+30 \\ TSA_B=110 \end{gathered}`

The total surface area of prism B is 110 sq. cm.

So option B is also correct.

Note that we have already found that the lateral surface area of prism A is 60 sq. cm.

Therefore, option C is also correct.

The total cross section area of prism A is calculated as,

`\begin{gathered} A_A=2(3*5) \\ A_A=30 \end{gathered}`

So the total surface area of prism A becomes,

`\begin{gathered} TSA_A=LSA_A+A_A \\ TSA_A=60+30 \\ TSA_A=90 \end{gathered}`

The total surface area of prism A is 90 sq. cm.

It is oberved that prism B has a larger surface area.

So, option D is also correct.

Hence, we can conclude that all the given statements are correct.