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