7:[["$","script",null,{"type":"application/ld+json","dangerouslySetInnerHTML":{"__html":"{\"@context\":\"https://schema.org\",\"@type\":\"Quiz\",\"name\":\"Quiz 4\",\"description\":\"Area and volume fundamentals.\",\"url\":\"https://theschoolofmathematics.com/quiz/psat-8-9-geometry-area-volume-quiz-4\",\"educationalLevel\":\"Advanced\",\"numberOfQuestions\":10,\"isAccessibleForFree\":true,\"about\":{\"@type\":\"Thing\",\"name\":\"Geometry and Trigonometry - Area and volume\"}}"}}],["$","script",null,{"type":"application/ld+json","dangerouslySetInnerHTML":{"__html":"{\"@context\":\"https://schema.org\",\"@type\":\"BreadcrumbList\",\"itemListElement\":[{\"@type\":\"ListItem\",\"position\":1,\"name\":\"Home\",\"item\":\"https://theschoolofmathematics.com\"},{\"@type\":\"ListItem\",\"position\":2,\"name\":\"Quizzes\",\"item\":\"https://theschoolofmathematics.com/quiz\"},{\"@type\":\"ListItem\",\"position\":3,\"name\":\"Quiz 4\",\"item\":\"https://theschoolofmathematics.com/quiz/psat-8-9-geometry-area-volume-quiz-4\"}]}"}}],["$","div",null,{"className":"bg-gradient-to-b from-white via-gray-50 to-white","children":["$","div",null,{"className":"container mx-auto px-4 py-8 md:py-12","children":[["$","div",null,{"className":"mb-12","children":["$undefined",["$","div",null,{"className":"mb-8","children":["$","h1",null,{"className":"text-4xl md:text-5xl lg:text-6xl font-bold text-gray-900 mb-4","children":"Quiz 4"}]}],["$","div",null,{"className":"bg-white rounded-2xl shadow-lg p-6 md:p-8 border border-gray-200","children":[["$","div",null,{"className":"text-lg md:text-xl text-gray-700 mb-8 leading-relaxed prose prose-lg max-w-none","dangerouslySetInnerHTML":{"__html":"

Area and volume fundamentals.

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Practice problems focused on area and volume concepts for PSAT 8/9.

"},"excerpt":{"rendered":"

Area and volume fundamentals.

"},"featured_media":0,"featured_media_url":"$undefined","acf":{"duree_estimee":"$undefined","niveau_difficulte":"Advanced","categorie":"Geometry and Trigonometry - Area and volume","nombre_questions":10,"score_minimum":70,"ordre_questions":"Fixe","questions":[{"id":"cmrk8f0qf0ydsjg8wdw1e1zh1","texte_question":"

A cylindrical container has a height of $$40$$ centimeters. The radius of container $$A$$ is $$10$$ centimeters, and the radius of container $$B$$ is $$50\\%$$ greater than the radius of container $$A$$. What is the volume, in cubic centimeters, of container $$B$$?

","type_question":"QCM","explication":"

Find the radius of container $$B$$. $$50\\%$$ greater than $$10$$ means multiply by $$1.5$$.

$$10 \\times 1.5=15$$

So, the radius of container $$B$$ is $$15$$ centimeters.

Use the volume formula for a cylinder.

$$V=\\pi r^2h$$

Substitute $$15$$ for the radius and $$40$$ for the height.

$$V=\\pi(15)^2(40)$$

Simplify.

$$15^2=225$$

$$V=225\\pi(40)$$

$$V=9000\\pi$$

Final answer: $$9000\\pi$$

","points":1,"temps_limite":60,"reponses":[{"texte":"$$$9000\\pi$$","correcte":true,"explication":"","imageUrl":"$undefined"},{"texte":"$$$12000\\pi$$","correcte":false,"explication":"","imageUrl":"$undefined"},{"texte":"

$$15000\\pi$$

","correcte":false,"explication":"","imageUrl":"$undefined"},{"texte":"

$$22500\\pi$$

","correcte":false,"explication":"","imageUrl":"$undefined"}]},{"id":"cmrk8f0qi0ydyjg8wcyitbrpv","texte_question":"

A triangle has a base length of $$30$$ centimeters and a height of $$20$$ centimeters. What is the area, in square centimeters, of the triangle?

","type_question":"QCM","explication":"

Use the formula for the area of a triangle.

$$A=\\frac{1}{2}bh$$

Substitute $$30$$ for the base and $$20$$ for the height.

$$A=\\frac{1}{2}(30)(20)$$

Multiply.

$$A=\\frac{1}{2}(600)$$

$$A=300$$

Final answer: $$300$$

","points":1,"temps_limite":60,"reponses":[{"texte":"$$$150$$","correcte":false,"explication":"","imageUrl":"$undefined"},{"texte":"$$$300$$","correcte":true,"explication":"","imageUrl":"$undefined"},{"texte":"

$$600$$

","correcte":false,"explication":"","imageUrl":"$undefined"},{"texte":"

$$900$$

","correcte":false,"explication":"","imageUrl":"$undefined"}]},{"id":"cmrk8f0qk0ye4jg8wpg56mh2k","texte_question":"

A circle has a circumference of $$20\\pi$$ centimeters. What is the diameter, in centimeters, of the circle?

","type_question":"TexteLibre","explication":"

Use the formula for circumference.

$$C=\\pi d$$

Substitute $$20\\pi$$ for the circumference.

$$20\\pi=\\pi d$$

Divide both sides by $$\\pi$$.

$$d=20$$

Final answer: $$20$$

","points":1,"temps_limite":60,"reponses":[{"texte":"

","correcte":true,"explication":"","imageUrl":"$undefined"}]},{"id":"cmrk8f0qn0ye7jg8wp5f0dgxz","texte_question":"

The floor of a gym has an area of $$900$$ square meters. A scale model is created where each side length is $$\\frac{1}{5}$$ of the actual floor. What is the area, in square meters, of the scale model?

","type_question":"QCM","explication":"

The side length scale factor is $$\\frac{1}{5}$$.

Area changes by the square of the side length scale factor.

$$\\left(\\frac{1}{5}\\right)^2=\\frac{1}{25}$$

Multiply the actual area by $$\\frac{1}{25}$$.

$$900 \\times \\frac{1}{25}=36$$

Final answer: $$36$$

","points":1,"temps_limite":60,"reponses":[{"texte":"$$$36$$","correcte":true,"explication":"","imageUrl":"$undefined"},{"texte":"$$$45$$","correcte":false,"explication":"","imageUrl":"$undefined"},{"texte":"

$$90$$

","correcte":false,"explication":"","imageUrl":"$undefined"},{"texte":"

$$180$$

","correcte":false,"explication":"","imageUrl":"$undefined"}]},{"id":"cmrk8f0qp0yedjg8w1wb4q4f1","texte_question":"

Rectangles $$JKLM$$ and $$NOPQ$$ are similar. The length of each side of rectangle $$NOPQ$$ is $$3$$ times the length of the corresponding side of $$JKLM$$. The area of rectangle $$JKLM$$ is $$8$$ square units. What is the area, in square units, of rectangle $$NOPQ$$?

","type_question":"QCM","explication":"

The side length scale factor is $$3$$.

For similar figures, the area scale factor is the square of the side length scale factor.

$$3^2=9$$

Multiply the original area by $$9$$.

$$8 \\times 9=72$$

Final answer: $$72$$

","points":1,"temps_limite":60,"reponses":[{"texte":"$$$24$$","correcte":false,"explication":"","imageUrl":"$undefined"},{"texte":"$$$48$$","correcte":false,"explication":"","imageUrl":"$undefined"},{"texte":"

$$72$$

","correcte":true,"explication":"","imageUrl":"$undefined"},{"texte":"

$$72$$

","correcte":false,"explication":"","imageUrl":"$undefined"}]},{"id":"cmrk8f0qr0yejjg8wigst5e7j","texte_question":"

A right circular cone has a height of $$12$$ centimeters and a base diameter of $$10$$ centimeters. The volume of this cone is $$n\\pi$$ cubic centimeters. What is the value of $$n$$?

","type_question":"TexteLibre","explication":"

The diameter is $$10$$ centimeters, so the radius is half of $$10$$.

$$r=\\frac{10}{2}$$

$$r=5$$

Use the formula for the volume of a cone.

$$V=\\frac{1}{3}\\pi r^2h$$

Substitute $$5$$ for the radius and $$12$$ for the height.

$$V=\\frac{1}{3}\\pi(5)^2(12)$$

Simplify.

$$5^2=25$$

$$V=\\frac{1}{3}\\pi(25)(12)$$

$$V=100\\pi$$

The volume is $$n\\pi$$, so $$n=100$$.

Final answer: $$100$$

","points":1,"temps_limite":60,"reponses":[{"texte":"

100

","correcte":true,"explication":"","imageUrl":"$undefined"}]},{"id":"cmrk8f0qu0yemjg8wqcurppii","texte_question":"

A cube has edge length $$12$$ inches and does not have a top face. What is the exterior surface area, in square inches, of this open cube?

","type_question":"TexteLibre","explication":"

A cube has $$6$$ faces.

Since the cube does not have a top face, there are $$5$$ exterior faces.

Find the area of one face.

$$12^2=144$$

Multiply by $$5$$.

$$5 \\times 144=720$$

Final answer: $$720$$

","points":1,"temps_limite":60,"reponses":[{"texte":"

720

","correcte":true,"explication":"","imageUrl":"$undefined"}]},{"id":"cmrk8f0qw0yepjg8wjh2r8zg7","texte_question":"

Rectangle $$UVWX$$ is similar to rectangle $$YZAB$$. The area of rectangle $$UVWX$$ is $$100$$ square inches, and the area of rectangle $$YZAB$$ is $$25$$ square inches. The longest side of rectangle $$UVWX$$ is $$20$$ inches. What is the length, in inches, of the longest side of rectangle $$YZAB$$?

","type_question":"QCM","explication":"

Find the area scale factor from rectangle $$UVWX$$ to rectangle $$YZAB$$.

$$\\frac{25}{100}=\\frac{1}{4}$$

The side length scale factor is the square root of the area scale factor.

$$\\sqrt{\\frac{1}{4}}=\\frac{1}{2}$$

Multiply the longest side of rectangle $$UVWX$$ by $$\\frac{1}{2}$$.

$$20 \\times \\frac{1}{2}=10$$

Final answer: $$10$$

","points":1,"temps_limite":60,"reponses":[{"texte":"

$$5$$

","correcte":false,"explication":"","imageUrl":"$undefined"},{"texte":"

$$10$$

","correcte":true,"explication":"","imageUrl":"$undefined"},{"texte":"

$$15$$

","correcte":false,"explication":"","imageUrl":"$undefined"},{"texte":"

$$20$$

","correcte":false,"explication":"","imageUrl":"$undefined"}]},{"id":"cmrk8f0qy0yevjg8wjerlmlrj","texte_question":"

A right rectangular prism has a length of $$12$$ centimeters, a width of $$5$$ centimeters, and a height of $$7$$ centimeters. What is the surface area, in square centimeters, of the prism?

","type_question":"TexteLibre","explication":"

Use the formula for the surface area of a rectangular prism.

$$SA=2(lw+lh+wh)$$

Substitute $$12$$ for the length, $$5$$ for the width, and $$7$$ for the height.

$$SA=2((12)(5)+(12)(7)+(5)(7))$$

Multiply.

$$SA=2(60+84+35)$$

Add inside the parentheses.

$$SA=2(179)$$

$$SA=358$$

Final answer: $$358$$

","points":1,"temps_limite":60,"reponses":[{"texte":"

358

","correcte":true,"explication":"","imageUrl":"$undefined"}]},{"id":"cmrk8f0r00yeyjg8w0neocjy7","texte_question":"

Right rectangular prism $$M$$ is similar to right rectangular prism $$N$$. The surface area of prism $$M$$ is $$32$$ square centimeters, and the surface area of prism $$N$$ is $$288$$ square centimeters. The volume of prism $$N$$ is $$216$$ cubic centimeters. What is the sum of the volumes of prisms $$M$$ and $$N$$?

","type_question":"TexteLibre","explication":"

Find the surface area scale factor from prism $$M$$ to prism $$N$$.

$$\\frac{288}{32}=9$$

Surface area changes by the square of the side length scale factor.

$$s^2=9$$

$$s=3$$

Volume changes by the cube of the side length scale factor.

$$3^3=27$$

So, the volume of prism $$N$$ is $$27$$ times the volume of prism $$M$$.

$$216=27V_M$$

Divide both sides by $$27$$.

$$V_M=8$$

Find the sum of the volumes.

$$216+8=224$$

Final answer: $$224$$

","points":1,"temps_limite":60,"reponses":[{"texte":"

224

","correcte":true,"explication":"","imageUrl":"$undefined"}]}]},"categories":["geometry-and-trigonometry-area-and-volume"],"date":"2026-06-04T09:04:49.485Z","modified":"2026-07-14T05:49:54.419Z"}}],["$","div",null,{"className":"container mx-auto px-4 pb-12","children":["$","$L18",null,{"targetType":"quiz","targetSlug":"psat-8-9-geometry-area-volume-quiz-4"}]}]]}]}]]

Quiz 4

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