Square and cube roots Transitional Reasoning Download PDF

Questions

1. 1.

   An environmental engineer designs a rectangular mounting bracket to hold two devices: a flat square solar collector with an area of 1024 cm2 and a sealed cubic data-logger with a volume of 1728 cm3. The length of the bracket equals the side length of the solar collector, and the width of the bracket equals the edge length of the cubic data-logger. What is the area of this rectangular mounting bracket?

   • A) 384 cm2
   • B) 448 cm2
   • C) 88 cm2
   • D) 320 cm2
2. 2.

   A city park features a flat square plaza with an area of 900 m² and a solid cubic art installation with a volume of 125 m³ located at its center. The park authority installs decorative bollard lights along the entire outer perimeter of the plaza such that the distance between any two consecutive lights is equal to the edge length of the cubic art installation. How many bollard lights are installed along the perimeter of the plaza?

   • A) 6
   • B) 18
   • C) 28
   • D) 24
3. 3.

   An interior designer creates a decorative floor border by placing 5 identical square ceramic tiles end to end in a straight line. Each square tile has an area of 576 cm2. Along an adjacent parallel line of the exact same total length, the designer arranges identical cubic display pedestals side by side, each having a volume of 3375 cm3. How many cubic pedestals are needed to match the total length of the tile border?

   • A) 6
   • B) 8
   • C) 10
   • D) 15
4. 4.

   An artist is designing two structural elements for a sculpture gallery: a square display panel and a freestanding cubic wireframe. The flat square panel has an area of $196\text{ dm}^2$ and will be bordered along all four edges with a continuous metallic strip. The cubic wireframe has an interior volume of $512\text{ dm}^3$ and is constructed using rigid metal rods along all twelve of its edges. What is the difference between the total length of metal rods needed for the cubic frame and the total length of metallic strip needed for the square panel?

   • A) 32 dm
   • B) 40 dm
   • C) 48 dm
   • D) 64 dm
5. 5.

   A student is building a display stand by centering a solid cubic wooden block on a flat square base plate. The volume of the cubic block is $216\text{ cm}^3$, and the surface area of the square base plate is $256\text{ cm}^2$. If the cubic block is positioned centrally so that its edges are parallel to the edges of the base plate, what is the distance between each side of the block's base and the nearest parallel edge of the plate?

   • A) $10\text{ cm}$
   • B) $7\text{ cm}$
   • C) $5\text{ cm}$
   • D) $4\text{ cm}$