Area and Volume Questions

Solution  : Circumradius Formula (R) = \(abc\over 4\Delta\) where R = radius of circumcircle described about a given triangle with sides a, b, c. \(\Delta\) = \(\sqrt{s(s – a)(s – b)(s – c)}\) and s = \(a + b + c\over 2\) where a, b and c are the sides of triangle.

Solution : Inradius Formula (r) = \(\Delta\over s\) Where r = radius of the circle inscribed in a given triangle \(\Delta\) = area of the given triangle \(\Delta\) = \(\sqrt{s(s – a)(s – b)(s – c)}\) s = half perimeter of the given triangle s = \(a + b + c\over 2\)  for all a,

Solution : Here radius = 10 cm We know that the surface area of hemisphere = \(3 \pi r^2\) = \(3 \times 3.14 \times 10 \times 10\) = 942 \(cm^2\)

Question : In a marriage ceremony of her daughter Poonam, Ashok has to make arrangements for the accommodation of 150 persons. For this purpose, he plans to build a conical tent in such a way that each person has 4 sq. meters of the space on ground and 20 cubic meters of air to breath.

Solution : Inner Radius (r) = \(24\over 2\) = 12 cm Outer Radius (R) = \(28\over 2\) = 14 cm Height of Pipe = 35 cm Volume = \(\pi (R^2 – r^2) h\) = \(\pi \times 52 \times 35\) = 5720 \(cm^3\) Mass of 1 \(cm^3\) wood = 0.6 kg Mass of 5720 \(cm^3\) wood

Solution : Lateral or Curved Surface Area of Cylinder = \(2 \pi rh\) \(\implies\) \(2 \pi rh\) = 94.2 \(\implies\) \(2 \pi r \times 5\) = 94.2  \(\implies\) r = 3 cm Given, height = 5 cm Volume of Cylinder = \(\pi r^2 h\) = \(\pi \times 9 \times 5\) = \(3.14 \times 9 \times

Solution : Circumference of the base cylindrical vessel = \(2\pi r\) \(\implies\)  \(2\pi r\) = 132    \(\implies\)  r = 21 cm Given, height = 25 cm Volume of cylinder = \(\pi r^2 h\) = \(\pi \times {21}^2 \times 25\) = 34650 \(cm^3\) Since 1litre = 1000 \(cm^3\) Therefore, It can hold 34.65 litres of

Solution : The formula for volume of cuboid of length l, breadth b and height h is \(lbh\). Read Post : Formula for Volume of cuboid – Derivation & Example Similar Questions What is the Formula for Surface Area of Cylinder ? What is the Formula for Surface Area of Cube ? What is the

Solution : The formula for the total suface area of cube of side a is \(6a^2\). And the formula for the lateral surface area of cube is \(4a^2\). Read Post : Formula for Surface Area of Cube – Derivation & Example Similar Questions What is the Formula for Volume of Cuboid ? What is the

Solution : The formula for surface area of a cuboid of length l, breadth b and height h is 2(lb + bh + hl). This is the total surface area of cuboid. The lateral surface area of cuboid is 2(l + b)h. Read Post : Formula for Surface Area of Cuboid – Derivation & Example