Now You Try

<p>Use tiles to build an area model that has length and width as indicated.</p><p>length = x + 4, width = x</p>

<p>Two cubes have a total volume of 72 cm<code class='latex inline'>^3</code>. Both cubes have whole-number side lengths.</p><p>a) Find the side length of each cube.</p><p>b) Find the total surface area of both cubes.</p>

<p>Use tiles to build an area model that has length and width as indicated.</p><p>length = x, width = x + 2</p>

<p>Geometry The expression <code class='latex inline'>\displaystyle \pi r^{2} h </code> represents the volume of a cylinder with radius <code class='latex inline'>\displaystyle r </code> and height <code class='latex inline'>\displaystyle h . </code></p><p>a. What is the volume, to the nearest tenth of a cubic inch, of the juice can at the right? Use <code class='latex inline'>\displaystyle 3.14 </code> for <code class='latex inline'>\displaystyle \pi </code>.</p><p>b. Reasoning About how many cubic inches, to the nearest tenth of a cubic inch, does a fluid ounce of juice fill?</p><img src="/qimages/12455" />

<p>A square has an unknown side length, x.</p><p>a) Write a simplified expression for its perimeter.</p><p>b) Write a simplified expression for its area.</p><p>c) If the area of the square is 25 m<code class='latex inline'>^2</code>, find the perimeter of the square.</p>

<p>a. Geometry A cone has a slant height <code class='latex inline'>\displaystyle \ell </code> of <code class='latex inline'>\displaystyle 11 \mathrm{~cm} </code> and a radius <code class='latex inline'>\displaystyle r </code> of <code class='latex inline'>\displaystyle 3 \mathrm{~cm} </code>. Use the expression <code class='latex inline'>\displaystyle \pi r(\ell+r) </code> to find the surface area of the cone. Use <code class='latex inline'>\displaystyle 3.14 </code> for <code class='latex inline'>\displaystyle \pi </code>. Round to the nearest tenth of a square centimeter.</p><p>b. Reasoning Does the surface area of the cone double if the radius doubles? If the slant height doubles? Explain.</p>

<p>The surface area of a prism is the sum of the areas of the faces of the prism. Write a formula for the surface area of the triangular prism at the right.</p><img src="/qimages/24126" />

<p>Use tiles to build an area model that has length and width as indicated.</p><p>length = x + 1, width = x + 3</p>

<p>Find the height <code class='latex inline'>h</code> or the area of the base <code class='latex inline'>B</code> of the solid. </p><img src="/qimages/42514" />

<p>Use tiles to build an area model that has length and width as indicated.</p><p>length = x + 2, width = x + 3</p>

<p>a) Build a volume model to represent a cube with length, width, and height all equal to 5 cm. Sketch the model and label the length, width, and height.</p><p>b) What is the volume? Write this as a power.</p><p>c) Write an expression for the area of one face as a power. Evaluate the area of one face.</p>

<p>The area of one face of a cube is 64 cm<code class='latex inline'>^2</code>.</p><p>a) What side length of the cube would give this area?</p><p>b) Determine the volume of the cube. Write this as a power.</p>

<p>a) Build a volume model to represent a cube with length, width, and height all equal to 3 cm. Sketch the model and label the length, width, and height.</p><p>b) What is the volume? Write this as a power.</p>

<p>Find the height <code class='latex inline'>h</code> or the area of the base <code class='latex inline'>B</code> of the solid. </p><img src="/qimages/42513" />

<p>The total surface area of all six faces of a cube is 96 cm<code class='latex inline'>^2</code>.</p><p>a) Determine the area of one face of the cube.</p><p>b) What side length of the cube would give this area?</p><p>c) Determine the volume of the cube. Write this as a power.</p>

<p>a) A cube has a volume of 125 cm<code class='latex inline'>^3</code>. Find the total surface area of all six faces.</p><p>b) A cube has a volume of 343 cm<code class='latex inline'>^3</code>. Find the total surface area of all six faces.</p>

<p>a) Build an area model to represent a square with length and width both equal to 5 cm. Sketch the model and label the length and width.</p><p>b) What is the area? Write this as a power.</p>