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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.

"},"explanation":null,"metaTitle":null,"metaDescription":null,"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":"cmrk8f0og0yc9jg8wukgnyoph","texte_question":"

The volume of right circular cylinder $$B$$ is $$40$$ cubic centimeters. What is the volume, in cubic centimeters, of a right circular cylinder with three times the radius and half the height of cylinder $$B$$?

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

Use the formula for the volume of a cylinder.

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

The radius is multiplied by $$3$$.

Since the radius is squared, the volume is multiplied by $$3^2$$. $$3^2=9$$

The height is multiplied by $$\\frac{1}{2}$$.

Find the total scale factor.

$$9 \\times \\frac{1}{2}=\\frac{9}{2}$$

Multiply the original volume by the scale factor.

$$40 \\times \\frac{9}{2}=180$$

Final answer: $$180$$

","points":1,"temps_limite":60,"reponses":[{"texte":"$$$20$$","correcte":false,"explication":"","imageUrl":"$undefined"},{"texte":"$$$40$$","correcte":false,"explication":"","imageUrl":"$undefined"},{"texte":"

$$180$$

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

$$360$$

","correcte":false,"explication":"","imageUrl":"$undefined"}]},{"id":"cmrk8f0oi0ycfjg8weyhlomyv","texte_question":"

Square $$C$$ has side lengths that are $$5$$ times the side lengths of square $$D$$. The area of square $$C$$ is $$k$$ times the area of square $$D$$. What is the value of $$k$$?

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

The side length scale factor is $$5$$.

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

$$k=5^2$$ Simplify.

$$k=25$$

Final answer: $$25$$

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

","correcte":true,"explication":"","imageUrl":"$undefined"}]},{"id":"cmrk8f0ol0ycijg8wevpr8iwh","texte_question":"

A sphere has a radius of $$\\frac{9}{2}$$ feet. What is the volume, in cubic feet, of the sphere?

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

Use the formula for the volume of a sphere.

$$V=\\frac{4}{3}\\pi r^3$$

Substitute $$\\frac{9}{2}$$ for the radius.

$$V=\\frac{4}{3}\\pi\\left(\\frac{9}{2}\\right)^3$$

Evaluate the power.

$$\\left(\\frac{9}{2}\\right)^3=\\frac{729}{8}$$

Substitute.

$$V=\\frac{4}{3}\\pi\\cdot\\frac{729}{8}$$

Simplify.

$$V=\\frac{2916}{24}\\pi$$

$$V=\\frac{243\\pi}{2}$$

Final answer: $$\\frac{243\\pi}{2}$$

","points":1,"temps_limite":60,"reponses":[{"texte":"$$$36\\pi$$","correcte":false,"explication":"","imageUrl":"$undefined"},{"texte":"$$$\\frac{243\\pi}{2}$$","correcte":true,"explication":"","imageUrl":"$undefined"},{"texte":"

$$243\\pi$$

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

$$972\\pi$$

","correcte":false,"explication":"","imageUrl":"$undefined"}]},{"id":"cmrk8f0on0ycojg8wujq6dr4c","texte_question":"

A circle has a radius of $$12$$ meters. What is the area, in square meters, of the circle?

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

Use the formula for the area of a circle.

$$A=\\pi r^2$$

Substitute $$12$$ for the radius.

$$A=\\pi(12)^2$$

Simplify.

$$12^2=144$$

$$A=144\\pi$$

Final answer: $$144\\pi$$

","points":1,"temps_limite":60,"reponses":[{"texte":"$$$24\\pi$$","correcte":false,"explication":"","imageUrl":"$undefined"},{"texte":"$$$144\\pi$$","correcte":true,"explication":"","imageUrl":"$undefined"},{"texte":"

$$288\\pi$$

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

$$1728\\pi$$

","correcte":false,"explication":"","imageUrl":"$undefined"}]},{"id":"cmrk8f0op0ycujg8wz4g4d447","texte_question":"

A right circular cylinder has a base diameter of $$10$$ centimeters and a height of $$9$$ centimeters. What is the volume, in cubic centimeters, of the cylinder?

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

Use the formula for the volume of a cylinder.

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

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

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

$$r=5$$

Substitute $$5$$ for the radius and $$9$$ for the height.

$$V=\\pi(5)^2(9)$$

Simplify.

$$5^2=25$$

$$V=25\\pi(9)$$

$$V=225\\pi$$

Final answer: $$225\\pi$$

","points":1,"temps_limite":60,"reponses":[{"texte":"$$$225\\pi$$","correcte":true,"explication":"","imageUrl":"$undefined"},{"texte":"$$$450\\pi$$","correcte":false,"explication":"","imageUrl":"$undefined"},{"texte":"

$$900\\pi$$

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

$$1800\\pi$$

","correcte":false,"explication":"","imageUrl":"$undefined"}]},{"id":"cmrk8f0p80yd0jg8wh9379413","texte_question":"

Parallelogram $$LMNO$$ is similar to parallelogram $$PQRS$$. The length of each side of parallelogram $$PQRS$$ is $$4$$ times the length of its corresponding side of parallelogram $$LMNO$$. The area of parallelogram $$LMNO$$ is $$3$$ square centimeters. What is the area, in square centimeters, of parallelogram $$PQRS$$?

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

The side length scale factor is $$4$$.

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

$$4^2=16$$

Multiply the original area by $$16$$.

$$3 \\times 16=48$$

Final answer: $$48$$

","points":1,"temps_limite":60,"reponses":[{"texte":"$$$12$$","correcte":false,"explication":"","imageUrl":"$undefined"},{"texte":"$$$24$$","correcte":false,"explication":"","imageUrl":"$undefined"},{"texte":"

$$36$$

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

$$48$$

","correcte":true,"explication":"","imageUrl":"$undefined"}]},{"id":"cmrk8f0pb0yd6jg8w6rsfrs0o","texte_question":"

A right circular cone has a volume of $$36\\pi$$ cubic centimeters and the area of its base is $$9\\pi$$ square centimeters. What is the slant height, in centimeters, of this cone?

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

Use the cone volume formula.

$$V=\\frac{1}{3}Bh$$

Substitute $$36\\pi$$ for the volume and $$9\\pi$$ for the base area.

$$36\\pi=\\frac{1}{3}(9\\pi)h$$

Simplify.

$$36\\pi=3\\pi h$$

Divide both sides by $$3\\pi$$.

$$h=12$$

Now use the base area to find the radius.

$$\\pi r^2=9\\pi$$

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

$$r^2=9$$

$$r=3$$

The radius, height, and slant height form a right triangle.

$$l^2=r^2+h^2$$

Substitute $$3$$ for the radius and $$12$$ for the height.

$$l^2=3^2+12^2$$

$$l^2=9+144$$

$$l^2=153$$

Take the square root.

$$l=\\sqrt{153}$$

Simplify.

$$l=3\\sqrt{17}$$

Final answer: $$3\\sqrt{17}$$

","points":1,"temps_limite":60,"reponses":[{"texte":"$$$3$$","correcte":false,"explication":"","imageUrl":"$undefined"},{"texte":"$$$4$$","correcte":false,"explication":"","imageUrl":"$undefined"},{"texte":"

$$5$$

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

$$3\\sqrt{17}$$

","correcte":true,"explication":"","imageUrl":"$undefined"}]},{"id":"cmrk8f0pe0ydcjg8ws0oq1zxs","texte_question":"

A cube has a surface area of $$96$$ square meters. What is the volume, in cubic meters, of the cube?

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

Use the formula for the surface area of a cube.

$$SA=6s^2$$

Substitute $$96$$ for the surface area.

$$96=6s^2$$

Divide both sides by $$6$$.

$$16=s^2$$

Take the square root.

$$s=4$$

Use the formula for the volume of a cube.

$$V=s^3$$

Substitute $$4$$ for the side length.

$$V=4^3$$

$$V=64$$

Final answer: $$64$$

","points":1,"temps_limite":60,"reponses":[{"texte":"$$$16$$","correcte":false,"explication":"","imageUrl":"$undefined"},{"texte":"$$$32$$","correcte":false,"explication":"","imageUrl":"$undefined"},{"texte":"

$$64$$

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

$$128$$

","correcte":false,"explication":"","imageUrl":"$undefined"}]},{"id":"cmrk8f0pg0ydijg8whjln35v6","texte_question":"

Square $$M$$ has a side length of $$10$$ centimeters. The perimeter of square $$N$$ is $$3$$ times the perimeter of square $$M$$. What is the length, in centimeters, of one side of square $$N$$?

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

Find the perimeter of square $$M$$.

$$P=4s$$

Substitute $$10$$ for the side length.

$$P=4(10)$$

$$P=40$$

The perimeter of square $$N$$ is $$3$$ times this amount.

$$3 \\times 40=120$$

Divide by $$4$$ to find one side length of square $$N$$.

$$\\frac{120}{4}=30$$

Final answer: $$30$$

","points":1,"temps_limite":60,"reponses":[{"texte":"$$$10$$","correcte":false,"explication":"","imageUrl":"$undefined"},{"texte":"$$$15$$","correcte":false,"explication":"","imageUrl":"$undefined"},{"texte":"

$$20$$

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

$$30$$

","correcte":true,"explication":"","imageUrl":"$undefined"}]},{"id":"cmrk8f0pi0ydojg8wl1tq7ts5","texte_question":"

A circle has a radius of $$5$$ inches. The area of the circle is $$b\\pi$$ square inches, where $$b$$ is a constant. What is the value of $$b$$?

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

Use the formula for the area of a circle.

$$A=\\pi r^2$$

Substitute $$5$$ for the radius.

$$A=\\pi(5)^2$$

Simplify.

$$5^2=25$$

$$A=25\\pi$$

The area is written as $$b\\pi$$.

$$b=25$$

Final answer: $$25$$

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

","correcte":true,"explication":"","imageUrl":"$undefined"}]}]},"categories":["geometry-and-trigonometry-area-and-volume"],"date":"2026-06-04T09:04:49.429Z","modified":"2026-07-14T05:49:54.347Z"}}],false,["$","div",null,{"className":"mt-10 mb-12","aria-label":"Advertisement","children":["$","div",null,{"className":"my-8 ","children":["$","$L19",null,{"adSlot":"1234567890","adFormat":"auto","fullWidthResponsive":true,"style":{"minHeight":"250px"}}]}]}]]}]}]]

Geometry and Trigonometry - Area and volume — Quiz 3

Questions in this quiz (10)