Find the total surface area of a right circular cone, if the height and radius of the cone are 63 cm and 16 cm, respectively.
1296π cm2
The total surface area of a cone is given by:
Surface area = πr(r + l),
where r is the radius and l is the slant height of the cone.
We are given the radius r = 16 cm and the height h = 63 cm. First, we calculate the slant height l using the Pythagorean theorem:
l = √(r2 + h2) = √(162 + 632) = √(256 + 3969) = √4225 = 65 cm
Now, substitute the values into the surface area formula:
Surface area = π × 16 × (16 + 65) = π × 16 × 81 = 1296π cm2
The total surface area of the cone is 1296π cm2.
Important Questions from Mensuration
The areas of three adjacent faces of a cuboidal tank are 3 m 2, 12 m 2 and 16 m 2. the capacity of the tank, in litres, is:
Volume of a cuboid is 4800 cm 3. If the height of this cuboid is 20 cm, then what will be the area of the base of cuboid ?
Two similar cubes have heights of 8 cm and 12 cm, respectively. If the capacity of the smaller cube is 80 cm 3, what is the capacity of the bigger cube (in cm 3)?
Three circles of radius 7 cm are kept touching each other. The string is tightly tied around these three circles. What is the length of the string?
Three circles of radius 6 cm are kept touching each other. The string is tightly tied around these three circles. What is the length of the string?
