Question
The radius and height of a right circular cone are in
the ratio 3: 4. If its curved surface area (in cm²) is 240 π, then its volume (in cm³) is:Solution
Curved surface area of cone = π r l Volume of cone = (1/3) π r2 h Slant height = √(h2 + r2 ) Let the radius and height of the cone be 3x and 4x Slant height = √[(4x)2 + (3x)2 ] ⇒ √(16x2 + 9x2 ) ⇒ √25x ⇒ 5x Curved suface area = π × 3x × 5x2 ⇒ 240 π = π × 15x ⇒ x2 = 16 ⇒ x = 4 Radius = 12 cm Height = 16 cm Slant height = 20 cm Volume of the cone = (1/3) × π × 144 × 16 ⇒ 48 × 16 × π ⇒ 768 π
What is the difference between (in m2) the area of a circular field of radius 14 metres and area of a rectangular piece of land having its di...
The curved surface area of a right cylinder is 3696 cm³. Its height is three times its radius. What is the capacity (in litres) of the cylinder? (T...
John had to multiply 'a' by 'b'. He however multiplied 'a' by 22.5 and obtained 423 as the product. Selina also had to multiply 'a' by 'b'. She however ...
The breadth of a rectangle is increased by 10 cm, it will become twice the length of the rectangle. If the new perimeter is 336 cm, then find the origin...
The sum of the total surface areas of two cubes is 1392 cm2. If the product of the length of their edges is 98 cm2, then find the ...
The angle of depression of the foot of a building from the top of a tower 54√3 m away is 30°. How high is the tower?
The perimeter of 4 squares is 24 cm, 36cm, 40 cm, and 44 cm respectively. What will be the area of the square having perimeter equal to sum of edges of ...
If each interior angle of a regular polygon is 135 degrees, then number of side of this polygon is
The perimeter of a rectangle of length 2(x + 5) cm and breadth 2(x + 2) cm is double the perimeter of a square of area 324 cm². Find the area of the re...
Perimeter of a rectangle is 70% more than that of a square of side 22 cm. If the difference between the length and breadth of the rectangle is 15 cm, re...