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Question 1 of 6
hard
A rectangular field is twice as long as it is wide. If the area is 288 m², find its perimeter.
Explanation: Let width=x, length=2x. Area=2x²=288 → x²=144 → x=12. Length=24, perimeter=2(24+12)=72
Question 2 of 6
hard
The area of an equilateral triangle is 36√3 cm². Find its side length.
Explanation: Area = (√3/4)a² = 36√3 → a²/4=36 → a²=144 → a=12
Question 3 of 6
hard
Three cubes of side 4 cm are joined end to end. Find the surface area of the resulting cuboid.
Explanation: Length=12, width=4, height=4. TSA=2(12×4+4×4+4×12)=2(48+16+48)=2×112=224
Question 4 of 6
hard
A cylinder and a cone have the same base radius and same height. If the volume of the cone is 50 cm³, find the volume of the cylinder.
Explanation: Volume cylinder = 3×volume cone = 150 cm³
Question 5 of 6
hard
A cylindrical pipe has inner diameter 14 cm and outer diameter 21 cm. Its length is 20 cm. Find the volume of metal used.
Explanation: Volume = πh(R²-r²) = 22/7×20×(10.5²-7²) = 22/7×20×(110.25-49) = 22/7×20×61.25 = 22×20×8.75 = 3850
Question 6 of 6
hard
The diagonal of a cube is 6√3 cm. Find its total surface area.
Explanation: Diagonal of cube = a√3 = 6√3 → a=6. TSA=6a²=6×36=216
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