GEOMETRY QUESTION PAPER THREE [New]

📖 Simple Geometry Practice Paper 📐

Test your fundamental geometry skills. Read each question carefully and try to solve it before revealing the solution. Good luck! 🍀

Question 1: Area of a Triangle 📏

A triangle has a base of 14 cm and a corresponding height of 8 cm. What is its area? 🧐

✅ Solution

The formula for the area of a triangle is given by:

$$ Area = \frac{1}{2} \times base \times height $$

We are given:

• Base (b) = 14 cm
• Height (h) = 8 cm

Plugging these values into the formula:

$$ Area = \frac{1}{2} \times 14 \times 8 $$ $$ Area = 7 \times 8 $$ $$ Area = 56 \text{ cm}^2 $$

So, the area of the triangle is 56 square centimeters. 💯

Question 2: Circumference of a Circle 🔴

Calculate the circumference of a circle with a radius of 7 meters. Use the value of Pi (\(\pi\)) as approximately \( \frac{22}{7} \). 🤔

✅ Solution

The formula for the circumference of a circle is:

$$ Circumference = 2 \times \pi \times r $$

We are given:

• Radius (r) = 7 m
• Pi (\(\pi\)) ≈ \( \frac{22}{7} \)

Substitute the values into the formula:

$$ Circumference = 2 \times \frac{22}{7} \times 7 $$

The 7 in the numerator and denominator cancel out:

$$ Circumference = 2 \times 22 $$ $$ Circumference = 44 \text{ meters} $$

Thus, the circumference of the circle is 44 meters. 🌍

Question 3: Pythagorean Theorem 📐

In a right-angled triangle, the length of the two shorter sides (legs) are 6 inches and 8 inches. What is the length of the longest side (the hypotenuse)?

✅ Solution

We use the Pythagorean theorem, which states that for a right-angled triangle with legs 'a' and 'b' and hypotenuse 'c':

$$ a^2 + b^2 = c^2 $$

Here, we have:

• a = 6 inches
• b = 8 inches

Let's find \(c^2\):

$$ 6^2 + 8^2 = c^2 $$ $$ 36 + 64 = c^2 $$ $$ 100 = c^2 $$

Now, we find 'c' by taking the square root of 100:

$$ c = \sqrt{100} $$ $$ c = 10 \text{ inches} $$

The length of the hypotenuse is 10 inches. ✨

Question 4: Volume of a Cylinder 🥫

Find the volume of a cylinder that has a radius of 5 cm and a height of 10 cm. Use the value of Pi (\(\pi\)) as approximately \(3.14\).

✅ Solution

The formula for the volume of a cylinder is:

$$ Volume = \pi \times r^2 \times h $$

We are given:

• Radius (r) = 5 cm
• Height (h) = 10 cm
• Pi (\(\pi\)) ≈ \(3.14\)

Substitute the values into the formula:

$$ Volume = 3.14 \times (5^2) \times 10 $$ $$ Volume = 3.14 \times 25 \times 10 $$ $$ Volume = 78.5 \times 10 $$ $$ Volume = 785 \text{ cm}^3 $$

The volume of the cylinder is 785 cubic centimeters. 🧪

Keep practicing! 🚀 Geometry is the key to understanding the world around us. 🌌