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PSAT Math : Prisms

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Example Questions

Example Question #242 : Geometry

Angie is painting a 2 foot cube for a play she is in. She needs $25\hspace{1 mm}mL$ of paint for every square foot she paints. How much paint does she need?

Possible Answers:

$100\hspace{1 mm}mL$

$1.041\overline{6}\hspace{1 mm}mL$

It is impossible to convert between metric units and feet.

$600\hspace{1 mm}mL$

None of the available answers

Correct answer:

$600\hspace{1 mm}mL$

Explanation:

First we must calculate the surface area of the cube. We know that there are six surfaces and each surface has the same area:

$Area=6(2^2)=6\times 4=24\hspace{1 mm}feet^2$

Now we will determine the amount of paint needed

$24\hspace{1 mm}feet^2\times \frac{25\hspace{1 mm}mL}{1\hspace{1 mm}foot^2}=600\hspace{1 mm}mL$

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Example Question #621 : Geometry

What is the surface area of an equilateral triangluar prism with edges of 6 in and a height of 12 in?

Let $\sqrt{3}=1.732$ and $\sqrt{2}=1.414$ .

Possible Answers:

$189.239\ in^{2}$

$247.176\ in^{2}$

$165.135\ in^{2}$

$268.732\ in^{2}$

$216.414\ in^{2}$

Correct answer:

$247.176\ in^{2}$

Explanation:

The surface area of the prism can be broken into three rectangular sides and two equilateral triangular bases.

The area of the sides is given by: $A=lw=12\cdot 6=72\ in^{2}$ , so for all three sides we get $\dpi{100} 216\ in^{2}$ .

The equilateral triangle is also an equiangular triangle by definition, so the base has congruent sides of 6 in and three angles of 60 degrees. We use a special right traingle to figure out the height of the triangle: 30 - 60 - 90. The height is the side opposite the 60 degree angle, so it becomes $3\sqrt{3}$ or 5.196.

The area for a triangle is given by $A=\frac{1}{2}bh$ and since we need two of them we get $A=bh=6\cdot 3\sqrt{3}=31.176\ in^{2}$ .

Therefore the total surface area is $216\ in^{2}+31.176\ in^{2}=247.176\ in^{2}$ .

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Example Question #1 : How To Find The Surface Area Of A Prism

What is the total surface area of a box without a lid, if the dimensions of the base of the box are $6\textup{ in by }10\textup{ in}$ , and the box is $5\textup{ in}$ tall?

Possible Answers:

$220\textup{ sq in}$

$280\textup{ sq in}$

$160\textup{ sq in}$

$360\textup{ sq in}$

$300\textup{ sq in}$

Correct answer:

$220\textup{ sq in}$

Explanation:

The surface area of a rectangular prism is 2lw+2lh+2wh . Our prism, however, is missing its top, so it will be . This gives us (10)(6)+2(10)(5)+2(6)(5)=220 .

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PSAT Math : Prisms

Study concepts, example questions & explanations for PSAT Math

All PSAT Math Resources

Example Questions

Example Question #242 : Geometry

Example Question #621 : Geometry

Example Question #1 : How To Find The Surface Area Of A Prism

All PSAT Math Resources

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