Question
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.
The correct answer is
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.
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Important Questions from Mensuration
- The volume of a wall that is 5 times as high as it is broad and 8 times as long as it is high is 12.8 cubic meters. Find the breadth of the wall.
- If the radius of a sphere is increased by 2 cm, then its surface area increases by 704 cm\(^2\). Using \(\pi = \frac{22}{7}\), find the radius of the sphere after the increase.
- What is the perimeter of an equilateral triangle with side 13 cm?
- The perimeter of a square is 76 m. Its area (in $m^2$) is:
- A cylindrical rod has an outer curved surface area of 1800 cm$^2$. If the length of the rod is 52 cm, then the outer radius (in cm) of the rod, correct to two places of decimal, is:
Take $\pi = \frac{22}{7}$
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