Cone Spheres

Question 1

What is the radius of the sphere mentioned?

Answer 1

5 cm

Question 2

What is the formula for the volume of a sphere?

Answer 2

V = 4/3 π r³

Question 3

Calculate the volume of a sphere with a radius of 5 cm.

Answer 3

V = 4/3 π (5)³ = 523.6 cm³

Question 4

What is the formula for the surface area of a sphere?

Answer 4

Surface Area = 4 π r²

Question 5

Find the surface area of a sphere with a radius of 5 cm.

Answer 5

Surface Area = 4 π (5)² = 100 π cm²

Question 6

What is the radius of the cone mentioned?

Answer 6

5 cm

Question 7

What is the height of the cone mentioned?

Answer 7

10 cm

Question 8

What is the formula for the volume of a cone?

Answer 8

V = (1/3) π r² h

Question 9

Calculate the volume of a cone with a radius of 5 cm and height of 10 cm.

Answer 9

V = (1/3) π (5)² (10) = 250 π cm³

Question 10

What is the formula for the total surface area of a cone?

Answer 10

Total Surface Area = πr² + πrl

Where r is the radius and l is the slant height.

Question 11

If the radius of a cone is 5 cm, what is the area of its base?

Answer 11

Area of base = π(5)² = 25π cm²

The area of a circle is calculated using the formula A = πr².

Question 12

What is the curved surface area of a cone?

Answer 12

Curved Surface Area = πrl

Where l is the slant height.

Question 13

Calculate the total surface area of a cone with a base area of 25 cm² and a curved surface area of 175.62 cm².

Answer 13

Total Surface Area = 25 + 175.62 = 200.62 cm²

The total surface area is the sum of the base area and the curved surface area.

Question 14

Fill in the blank: The volume of a cone is given by the formula _______.

Answer 14

Volume = (1/3)πr²h

Where r is the radius and h is the height.

Question 15

If the volume of a cone is 1145.1 cm³ and the height is 38 cm, how do you find the radius?

Answer 15

Use the formula r = √((3V)/(πh))

Rearranging the volume formula gives the radius.

Question 16

What is the relationship between radius and volume in a cone?

Answer 16

Volume is directly related to the cube of the radius

As radius increases, the volume increases significantly due to the cubic relationship.

Question 17

True or False: The slant height of a cone can be calculated using the formula l = √(r² + h²).

Answer 17

True

This is derived from the Pythagorean theorem.

Question 18

What is the slant height of a cone with a radius of 4.5 cm and a height of 38 cm?

Answer 18

l = √(4.5² + 38²)

Calculate l using the Pythagorean theorem.

Question 19

What is the formula for calculating the surface area of a sphere?

Answer 19

4πr²

Question 20

If a sphere has a surface area of 254 cm², what is the radius?

Answer 20

5.76 cm

Question 21

What is the surface area of a sphere with a radius of 4.5 cm?

Answer 21

254 cm²

Question 22

The surface area of a sphere is given as 724 cm². What is the radius?

Answer 22

7.2 cm

Question 23

Fill in the blank: The volume of a sphere can be calculated using the formula _______.

Answer 23

4/3πr³

Question 24

What is the volume of a sphere with a radius of 5.76 cm?

Answer 24

2.4 cm³

Question 25

True or False: The surface area of a sphere increases with the square of the radius.

Answer 25

True

Question 26

If the radius of a sphere is doubled, how does the surface area change?

Answer 26

It quadruples.

Question 27

What is the relationship between surface area and volume for a sphere?

Answer 27

Surface area increases with the square of the radius; volume increases with the cube of the radius.