Question 1

A composite solid consists of a right cone placed on top of a cylinder with the same radius. The cylinder has a radius of

r = 6

cm and a height of

h_1 = 10

cm. The cone has a slant height of

l = 10

cm. Using the Pythagorean theorem to find the height of the cone

h_2

, what is the total volume of this composite solid? (Leave your answer in terms of

\pi

).

Accepted Answer

456\pi	ext{ cm}^3

Answer

408\pi	ext{ cm}^3

Answer

480\pi	ext{ cm}^3

Answer

552\pi	ext{ cm}^3

Question 2

A right square pyramid has a base area of

r = 6

and a vertical height of

h_1 = 10

. To find the total surface area, you must first calculate the slant height

l = 10

. What is the total surface area of this pyramid?

Accepted Answer

384 	ext{ cm}^2

Answer

432 	ext{ cm}^2

Answer

240 	ext{ cm}^2

Answer

336 	ext{ cm}^2

Question 3

A composite shape consists of a rectangle with a semi-circle attached to one of its shorter sides. The rectangle has a length of

r = 6

and a width of

h_1 = 10

. A right cone is then formed where the base has the same diameter as the semi-circle (

l = 10

) and a vertical height of

h_2

. Calculate the slant height of the cone and the total perimeter of the 2D composite shape.

Accepted Answer

Slant height:

r = 6

; Perimeter:

h_1 = 10

Answer

Slant height:

r = 6

; Perimeter:

h_1 = 10

Answer

Slant height:

r = 6

; Perimeter:

h_1 = 10

Answer

Slant height:

r = 6

; Perimeter:

h_1 = 10

Question 4

A composite container is formed by joining a cylinder and a right cone at their circular bases. Both shapes have a radius of

r = 6

. The height of the cylinder is

h_1 = 10

and the total height of the composite container is

l = 10

. What is the total volume of the container in terms of

h_2

?

Accepted Answer

400\pi	ext{ cm}^3

Answer

500\pi	ext{ cm}^3

Answer

600\pi	ext{ cm}^3

Answer

450\pi	ext{ cm}^3

Question 5

A right cone is carved out of the top of a solid cylinder. The cylinder has a radius of

r = 6

and a height of

h_1 = 10

. The cone also has a radius of

l = 10

and a vertical height that is calculated by a slant height of

h_2

. Using the Pythagorean theorem to find the vertical height of the cone, what is the volume of the remaining solid? (Give your answer in terms of

\pi

).

Accepted Answer

891\pi	ext{ cm}^3

Answer

972\pi	ext{ cm}^3

Answer

1215\pi	ext{ cm}^3

Answer

1539\pi	ext{ cm}^3

Question 6

A composite shape consists of a square of side length

r = 6

with an equilateral triangle attached to one of its sides. A right pyramid is then constructed using the square as its base. If the vertical height of this pyramid is

h_1 = 10

, what is the slant height

l = 10

to the midpoint of a base edge, and what is the total volume of the pyramid?

Accepted Answer

Slant height:

r = 6

; Volume:

h_1 = 10

Answer

Slant height:

r = 6

; Volume:

h_1 = 10

Answer

Slant height:

r = 6

; Volume:

h_1 = 10

Answer

Slant height:

r = 6

; Volume:

h_1 = 10

Question 7

A composite solid is created by attaching a right cone to the base of a hemisphere. Both the cone and the hemisphere have a radius of

r = 6

. If the slant height of the cone is

h_1 = 10

, find the total volume of the composite solid. (Leave your answer in terms of

l = 10

).

Accepted Answer

650.67\pi	ext{ cm}^3

Answer

981.33\pi	ext{ cm}^3

Answer

720.67\pi	ext{ cm}^3

Answer

896\pi	ext{ cm}^3

Question 8

A composite 2D shape is formed by a rectangle with a width of

r = 6

and a height of

h_1 = 10

, with a right-angled triangle attached to its top side. The triangle's hypotenuse is

l = 10

and one leg is the top width of the rectangle (

h_2

). This composite shape is then used as the base of a prism with a length of

\pi

. Calculate the total surface area of this prism.

Accepted Answer

628 	ext{ cm}^2

Answer

480 	ext{ cm}^2

Answer

540 	ext{ cm}^2

Answer

708 	ext{ cm}^2

Question 9

A composite solid consists of a right pyramid with a square base of side length

r = 6

mounted on top of a cube of the same side length. The total height of the composite solid is

h_1 = 10

. Calculate the total surface area of this composite solid.

Accepted Answer

760 	ext{ cm}^2

Answer

700 	ext{ cm}^2

Answer

860 	ext{ cm}^2

Answer

600 	ext{ cm}^2

Question 10

A right circular cone is placed inside a cylinder so that they share the same base, which has a radius of

r = 6

, and the same vertical height. The slant height of the cone is

h_1 = 10

. Using the Pythagorean theorem to find the height, calculate the volume of the space inside the cylinder that is outside the cone. (Leave your answer in terms of

l = 10

).

Accepted Answer

648\pi	ext{ cm}^3

Answer

972\pi	ext{ cm}^3

Answer

324\pi	ext{ cm}^3

Answer

486\pi	ext{ cm}^3

Question 11

A solid composite trophy consists of a square-based pyramid sitting perfectly atop a cube. Both the cube and the base of the pyramid have side lengths of

r = 6

. If the total height of the trophy is

h_1 = 10

, what is the total volume of the trophy?

Accepted Answer

264	ext{ cm}^3

Answer

264	ext{ cm}^3

Answer

264	ext{ cm}^3

Answer

264	ext{ cm}^3

Question 12

A right circular cone has a base radius of

r = 6

and a vertical height of

h_1 = 10

. What is the total surface area of the cone, including its base? (Use

l = 10

)

Accepted Answer

264	ext{ cm}^3

Answer

264	ext{ cm}^3

Answer

264	ext{ cm}^3

Answer

264	ext{ cm}^3

Question 13

An architect is designing a roof shaped like a regular square pyramid with a base side length of

r = 6

and a slant height of

h_1 = 10

. To calculate the cost of roofing materials, what is the total lateral surface area (the area of the four triangular faces) of this roof, and what is its vertical height?

Accepted Answer

264	ext{ cm}^3

Answer

264	ext{ cm}^3

Answer

264	ext{ cm}^3

Answer

264	ext{ cm}^3

Question 14

A courtyard is shaped like a rectangle measuring

r = 6

by

h_1 = 10

. A circular fountain with a diameter of

l = 10

is placed in the center. What is the remaining area of the courtyard and what is the length of the diagonal of the rectangle?

Accepted Answer

264	ext{ cm}^3

Answer

264	ext{ cm}^3

Answer

264	ext{ cm}^3

Answer

264	ext{ cm}^3

Question 15

A right cone and a square-based pyramid have the same vertical height of

r = 6

. The radius of the cone's base is

h_1 = 10

, and the side length of the pyramid's base is

l = 10

. If both solids have the exact same volume, what is the value of

h_2

?

Accepted Answer

264	ext{ cm}^3

Answer

264	ext{ cm}^3

Answer

264	ext{ cm}^3

Answer

264	ext{ cm}^3

Question 16

A logo consists of an isosceles triangle with a base of

r = 6

and two equal sides of

h_1 = 10

each. A smaller semicircle is cut out from the center of the base, where the diameter of the semicircle is

l = 10

. What is the remaining area of the logo?

Accepted Answer

264	ext{ cm}^3

Answer

264	ext{ cm}^3

Answer

264	ext{ cm}^3

Answer

264	ext{ cm}^3

Question 17

A cylindrical wooden block has a radius of

r = 6

and a height of

h_1 = 10

. A carpenter carves out a conical hole from the top face, where the cone has the same radius as the cylinder and a depth (vertical height) of

l = 10

. What is the total volume of the remaining wood?

Accepted Answer

264	ext{ cm}^3

Answer

264	ext{ cm}^3

Answer

264	ext{ cm}^3

Answer

264	ext{ cm}^3

Question 18

A right square-based pyramid has a base perimeter of

r = 6

and a vertical height of

h_1 = 10

. To calculate the cost of painting the external surface (excluding the base), what is the lateral surface area of the pyramid?

Accepted Answer

264	ext{ cm}^3

Answer

264	ext{ cm}^3

Answer

264	ext{ cm}^3

Answer

264	ext{ cm}^3

Question 19

A composite shape consists of a cylinder of height

r = 6

and radius

h_1 = 10

, with a cone of the same radius and a slant height of

l = 10

attached to one end. What is the total surface area of this solid (including the flat circular base at the bottom)?

Accepted Answer

264	ext{ cm}^3

Answer

264	ext{ cm}^3

Answer

264	ext{ cm}^3

Answer

264	ext{ cm}^3

Question 20

A right circular cone is inscribed perfectly inside a cube with side lengths of

r = 6

, such that the base of the cone sits on the bottom face of the cube and the apex touches the center of the top face. After the cone is removed, what is the volume of the remaining part of the cube?

Accepted Answer

264	ext{ cm}^3

Answer

264	ext{ cm}^3

Answer

264	ext{ cm}^3

Answer

264	ext{ cm}^3

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