Practice Questions
The area of a square is 64 sq cm. What is its perimeter?
Side = $\\sqrt{64} = 8$. Perimeter = $4 \\times 8 = 32$ cm.
A circle has a radius of 7 cm. What is its area? (Use $\\pi = 22/7$)
Area = $\\pi r^2 = \\frac{22}{7} \\times 7^2 = \\frac{22}{7} \\times 49 = 154$ sq cm.
What is the volume of a cylinder with radius 3 cm and height 10 cm? (Use $\\pi = 3.14$)
Volume = $\\pi r^2 h = 3.14 \\times 9 \\times 10 = 282.6$ cu cm.
A cube has a volume of 125 cubic cm. What is its total surface area?
Side = $\\sqrt[3]{125} = 5$. TSA = $6a^2 = 6 \\times 25 = 150$ sq cm.
The length of a rectangle is 20% more than its breadth. If the perimeter is 88 cm, find its area.
Let breadth = b, length = $1.2b$. Perimeter = $2(1.2b + b) = 4.4b = 88 \Rightarrow b = 20$, length = 24. Area = $20 × 24 = 480$ cm².
A cylindrical tank of radius 0.7 m and height 10 m is filled with water. How many litres does it contain? (Use π = 22/7)
Volume = $πr^2h = (22/7) × 0.49 × 10 = 15.4$ m³. $1$ m³ = $1000$ L. Capacity = $15.4 × 1000 = 15400$ L.
A solid cube is melted and recast into smaller cubes of side 2 cm. If original side was 8 cm, how many smaller cubes are formed?
Volume of original cube = $8^3 = 512$ cm³. Volume of small cube = $2^3 = 8$ cm³. Number = $512/8 = 64$.
The area of a circle is 154 cm². Find its circumference. (Use π = 22/7)
$πr^2 = 154 \Rightarrow r^2 = 154 × 7/22 = 49 \Rightarrow r = 7$. Circumference = $2πr = 2 × 22/7 × 7 = 44$ cm.
A cone and a cylinder have the same base radius and height. Find the ratio of their volumes.
Volume of cone = $(1/3)πr^2h$. Volume of cylinder = $πr^2h$. Ratio = $1:3$.
A rectangular park 60 m × 40 m has a path of width 5 m running all around inside it. Find the area of the path.
Outer area = $60 × 40 = 2400$ m². Inner dimensions = $60-10=50$ m, $40-10=30$ m. Inner area = $50 × 30 = 1500$ m². Path area = $2400 - 1500 = 900$ m².
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