SaiBook.us Geometry

Lesson Example Discussion Quiz: Class Homework

Example

Title: Surface area of 3D shapes(Cube, cuboid, Cone)

Grade: 4-a Lesson: S3-L1

Explanation: The best way to understand geometry is by looking at some examples. Take turns and read each example for easy understanding.

Examples:

What is the height of a cone if its radius is 12 units and its curved surface area is 524 square units? (Use π = 3.14)

Step 1a

Given that CSA = 524 square units and radius (r) = 12 units.

The formula for the curved surface area of a cone: CSA = \$π times r times l\$

Substitute these values into the formula:

524 = \$3.14 \times 12 \times l\$

524 = \$37.68 \times l\$

$1a$

Explanation: In this step, with a known curved surface area (CSA) of 524 square units and a radius (r) of 12 units, we apply the cone CSA formula, yielding 524 = \$3.14 times 12 times "l"\$, which simplifies to 524 = \$37.68 times "l"\$.

Step 1b

Solve for slant height(l) divide 37.68 on both sides of the equation: \$524/37.68\$ = \$(37.68 \times l)/37.68\$

l = 13.9 units

Explanation: In this step, solving for the slant height involves dividing both sides of the equation by 37.68. This simplifies to l = 13.9 units.

Step 1c

To find the height (h), you can use the Pythagorean theorem: h = \$\sqrt(l^2 - r^2\$

Now plug the values into the formula: h = \$\sqrt(13.9^2 - 12^2)\$

h = \$\sqrt(193.21 - 144)\$

h = \$ \sqrt(49.31)\$

h = 7 units

Therefore, the height of the cone is approximately 7 units.

Explanation: In this stage, determine the height (h) using the Pythagorean theorem: h = \$\sqrt(l^2 - r^2\$. Substituting values yields approximately 7 units. Hence, the cone’s height is approximately 7 units.