Question

A sector of a circle of radius 7 cm subtend an angle 270 degree at the centre of the circle is used to form a cone
A find the base radius of the cone calculate the total surface area of the cone to the nearest square centimetre

Answer 1

AAAaannndd the bot gets it wrong yet again!

cone base radius r = 7 * (270/360) = 21/4
cone slant height s = 7
cone area = πr(r+s) = 21/4 π (21/4 + 7) = 1029/16 π = 202.04

Answer 2

Beans and garri

Answer 3

a) Base radius of the cone =7 cm
b) Surface area of the cone(*×7²)+(*×7×14) =530cm²

Answer 4

Base radius of the cone = 7 cm

Surface area of the cone = (π x 7^2) + (π x 7 x 14) = 539 cm^2

Answer 5

I'm sorry, I don't understand what you mean. Could you please provide more context or information?

Answer 6

The calculation in part (b) is incorrect.

The correct formula for the surface area of a cone is πr(r+s), where r is the base radius and s is the slant height of the cone.

Using the value of r = 7 cm given in part (a), we need to find the value of s to calculate the surface area.

We can use the Pythagorean theorem, which states that for a right triangle with legs a and b and hypotenuse c, a^2 + b^2 = c^2. In this case, the triangle formed by the slant height, the radius, and the height of the cone is a right triangle.

Since the angle subtended by the sector at the center is 270 degrees, the angle at the apex of the cone is 90 degrees. Therefore, the height of the cone is equal to the radius, or h = r = 7 cm.

Using the Pythagorean theorem, we have s^2 = r^2 + h^2 = 7^2 + 7^2 = 98. Taking the square root of both sides, we have s = √98 = 7√2 cm.

Now we can calculate the surface area of the cone:

Surface area = πr(r+s) = π(7)(7 + 7√2) ≈ 214.97 cm^2 (rounded to two decimal places)