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
In a circular garden of radius 15 m, a path of 2 m wide has to be made inside the garden at the rate of ₹ 24 per sq. m. The cost of making the path is: (Take π = \(\frac{22}{7}\) )
A hollow cylinder with outer radius 4 cm and height 2 cm is made up of 1 cm thick metal sheet. What is the volume of metal used? (Take π = \(\frac{22}{7}\))
The length and breadth of a rectangular field are in the ratio 4 : 3. If the cost of cultivating the field at ₹2 per m 2is ₹600, then the length of the field is:
A cylindrical tank has a capacity of 5632 m3. If the diameter of its base is 8 m, what is the depth of the cylindrical tank? (Use π = \(\frac{22}{7}\))
Find the surface area of a sphere whose diameter is equal to 28 cm.
