Gr 10 Math Ch 10: Right Pyramids, Cones and Spheres

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What is the formula for calculating the surface area of a right cone?

$ ext{Area of base} + ext{Area of walls}$ (correct)
$ ext{Area of base} + 2 ext{Area of sides}$
$4rac{1}{3} imes ext{Area of base}$
$rac{1}{3} imes ext{Area of base} imes ext{Height}$

Which of the following descriptions accurately defines a right pyramid?

A pyramid with a circular base and apex not perpendicular to the base
A pyramid that has all sides perpendicular to its base
A pyramid with a polygon as its base and apex perpendicular to the base's center (correct)
A geometric shape with balanced triangular faces and no apex

What is the surface area formula for a square pyramid?

$b(b + 2h_s)$ (correct)
$4 imes rac{1}{2} b h_s$
$2b + 2h_s$
$b^2 + rac{1}{2} b h_s$

What factor is used to find the volume of a triangular pyramid?

$rac{1}{3} imes ext{Area of the base} imes H$ (D) Signup and view all the answers

How do you calculate the volume of a right cone?

$rac{1}{3} imes ext{Area of base} imes H$ (A) Signup and view all the answers

Which formula correctly represents the surface area of a sphere?

$4 ext{π}r^2$ (C) Signup and view all the answers

What does the apex of a pyramid refer to?

The point where all faces converge (D) Signup and view all the answers

Which of the following characteristics is exclusive to spheres?

All points on the surface are equidistant from the center (D) Signup and view all the answers

What is the volume formula for a square pyramid?

$\frac{1}{3} b^2 H$ (B) Signup and view all the answers

How does the surface area of a right cone relate to its circular base?

It equals the area of the base plus the area of the circular wall. (C) Signup and view all the answers

For a triangular pyramid, which components are included in the surface area formula?

Base area and area of the three side triangles. (B) Signup and view all the answers

What distinguishes the apex of a right pyramid from that of a cone?

In a right pyramid, the apex is above the center of any polygon base. (B) Signup and view all the answers

What is the correct surface area formula for a sphere?

$4\pi r^2$ (C) Signup and view all the answers

Which of the following statements about volume is true for a right cone?

The volume is equal to the area of the base times the height. (A) Signup and view all the answers

Which component does NOT contribute to the surface area of a square pyramid?

Volume of the pyramid. (A) Signup and view all the answers

When comparing the surfaces of a square pyramid and a triangular pyramid, what differs in their surface area calculations?

The number of triangular faces influencing the surface area. (C) Signup and view all the answers

What is the primary difference between a right pyramid and a right cone in terms of base shape?

A right pyramid has a polygonal base, while a right cone has a circular base. (C) Signup and view all the answers

In the surface area formula for a square pyramid, what does the variable $h_s$ represent?

The height of the triangular side. (D) Signup and view all the answers

What is the surface area of a sphere in terms of its radius $r$?

4πr^2 (D) Signup and view all the answers

Which of the following correctly expresses the volume of a triangular pyramid?

$rac{1}{3} imes rac{1}{2} b h imes H$ (A) Signup and view all the answers

How is the volume of a sphere expressed in terms of its radius $r$?

$rac{4}{3} imes ext{π} imes r^3$ (B) Signup and view all the answers

Which of the following statements about the surface area of a right cone is incorrect?

The surface area consists of only the lateral area. (A) Signup and view all the answers

In which situation does the formula for the volume of a square pyramid apply?

When the base is a square. (C) Signup and view all the answers

What is the correct volume formula for a triangular pyramid?

$\frac{1}{3} \left(\frac{1}{2} b h\right) H$ (B) Signup and view all the answers

In the surface area formula for a right cone, what does the term $\pi r h$ represent?

The lateral area of the cone (B) Signup and view all the answers

Which component is included in the surface area calculation of a square pyramid?

The area of the triangular sides (A) Signup and view all the answers

For a sphere, what does the formula $4\pi r^2$ represent?

The surface area of the sphere (B) Signup and view all the answers

How does the volume of a square pyramid relate to its base area and height?

It's one third of the product of the base area and height. (D) Signup and view all the answers

What defines a right pyramid as opposed to a regular pyramid?

The apex must be directly above the center of the base (D) Signup and view all the answers

Which of the following is not a characteristic of spheres?

They appear different from varying angles (B) Signup and view all the answers

What does the variable $h_s$ represent in the surface area formula for a square pyramid?

The height of the triangular side (A) Signup and view all the answers