Question

The base of a right circular cone has a radius of 8 cm and a slant height of 12 cm. If the radius and the slant height of the right circular cone are each multiplied by 9, what is the surface area of the new cone divided by the surface area of the original cone? Select one: a. 72 b. 18 c. 96 d. 81

Answer 1

Upon scaling the radius and slant height of a cone by 9, the surface area of the new cone is 81 times the area of the original cone. Hence, the answer is d. 81.

Step-by-step explanation:

To find out how the surface area of a right circular cone changes when its dimensions are scaled, let's calculate the surface area before and after the transformation.

The surface area of a cone (A) is given by the formula A = πr(r + l), where r is the radius and l is the slant height. Initially, we have r = 8 cm and l = 12 cm. After scaling, r = 8 cm × 9 = 72 cm and l = 12 cm × 9 = 108 cm.

The surface area of the original cone is A(original) = π × 8 cm × (8 cm + 12 cm) = π × 8 cm × 20 cm.

The surface area of the new cone is A(new) = π × 72 cm × (72 cm + 108 cm) = π × 72 cm × 180 cm.

To find the ratio of the new surface area to the original, we divide A(new) by A(original) and simplify: Ratio = (A(new) / A(original)) = (π × 72 cm × 180 cm) / (π × 8 cm × 20 cm) = (72 × 180) / (8 × 20) = 81. Hence, the answer is d. 81.

Answer 2

I am not quite sure how to do this, but I think it is this way:

You know that radius in the cone is 8 cm, and slant height is 12 cm.You must multiply 8 cm with 12 cm, because you must take height multiplied with radius.

8 x 12 = 96 cm
So, the answer is C, I think.