Free Printable Equations Pyramid

1.

The total surface area of this pyramid equals:

a)

$a^2+4\cdot\frac{1}{2}ah$

b)

$a^2+\frac{1}{2}ah$

c)

$a^2\cdot H$

d)

$\frac{1}{3}\cdot a^2\cdot H$

2.

The volume of this pyramid equals:

a)

$\frac{1}{3}\cdot a^2\cdot h$

b)

$\frac{1}{3}\cdot a^2\cdot H$

c)

$a^2\cdot H$

d)

$\frac{1}{3}\cdot a^2\cdot b$

3.

The surface area of a single lateral face of this pyramid equals:

a)

$\frac{1}{2}ab$

b)

$ab$

c)

$\frac{1}{2}ah$

d)

$aH$

4.

For this regular pyramid it is true that:

a)

$a^2+H^2=b^2$

b)

$\left(\frac{1}{2}a^2\right)+H^2=b^2$

c)

$\left(\frac{1}{2}a\right)^2+b^2=h^2$

d)

$\left(\frac{1}{2}a\right)^2+h^2=b^2$

5.

The total surface area of this pyramid equals:

a)

$\frac{a^2\sqrt{3}}{4}+3\cdot\frac{1}{2}ah$

b)

$\frac{a^2\sqrt{3}}{4}+3\cdot\frac{1}{2}aH$

c)

$a^2\sqrt{3}+3\cdot ah$

d)

$\frac{a^2\sqrt{3}}{2}+3\cdot\frac{1}{2}ah$

6.

The volume of this pyramid equals:

a)

$\frac{a^2\sqrt{3}}{4}\cdot H$

b)

$\frac{1}{3}\cdot\frac{a^2\sqrt{3}}{4}\cdot H$

c)

$\frac{1}{3}\cdot\frac{a^2\sqrt{3}}{2}\cdot H$

d)

$\frac{a^2\sqrt{3}}{4}\cdot h$

7.

The total surface area of this pyramid equals:

a)

$\frac{a^2\sqrt{3}}{4}+\frac{1}{2}ah$

b)

$\frac{a^2\sqrt{3}}{4}+6\cdot\frac{1}{2}ah$

c)

$6\cdot\frac{a^2\sqrt{3}}{4}+6\cdot\frac{1}{2}ah$

d)

$6\cdot\frac{a^2\sqrt{3}}{4}+\frac{1}{2}ah$

8.

The volume of this pyramid equals:

a)

$\frac{1}{3}\cdot6\cdot\frac{a^2\sqrt{3}}{2}\cdot H$

b)

$6\cdot\frac{a^2\sqrt{3}}{4}\cdot H$

c)

$\frac{1}{3}\cdot6\cdot\frac{a^2\sqrt{3}}{4}\cdot h$

d)

$\frac{1}{3}\cdot6\cdot\frac{a^2\sqrt{3}}{4}\cdot H$

9.

The area of a single lateral face of this pyramid equals:

a)

$\frac{1}{2}ah$

b)

$\frac{1}{2}ab$

c)

$\frac{1}{2}aH$

d)

$\frac{1}{2}bh$

10.

The area of the cross-section you can see in the picture equals:

a)

$\frac{1}{2}ah$

b)

$\frac{1}{2}aH$

c)

$\frac{1}{2}ab$

d)

$\frac{1}{2}hH$

11.

For this regular pyramid it is true that:

a)

$a^2+H^2=b^2$

b)

$a^2+H^2=h^2$

c)

$\left(\frac{1}{2}a\right)^2+H^2=h^2$

d)

$\left(\frac{1}{2}a\right)^2+h^2=H^2$

12.

The area of the cross-section you can see in the picture equals:

a)

$\frac{1}{2}\cdot a\cdot b$

b)

$\frac{1}{2}\cdot a\sqrt{2}\cdot h$

c)

$\frac{1}{2}\cdot a\cdot H$

d)

$\frac{1}{2}\cdot a\sqrt{2}\cdot H$

13.

For this regular pyramid it is true that:

a)

$\left(\frac{a\sqrt{2}}{2}\right)^2+H^2=b^2$

b)

$\left(\frac{a\sqrt{2}}{2}\right)^2+b^2=H^2$

c)

$\left(a\sqrt{2}\right)^2+H^2=b^2$

d)

$\left(a\sqrt{2}\right)^2+b^2=H^2$

14.

The area of the cross-section you can see in the picture equals:

a)

$\frac{1}{2}\cdot a\sqrt{2}\cdot H$

b)

$\frac{1}{2}\cdot\frac{a\sqrt{3}}{2}\cdot H$

c)

$\frac{1}{2}\cdot a\cdot H$

d)

$\frac{1}{2}\cdot h\cdot b$

15.

For this regular pyramid it is true that:

a)

$\left(\frac{1}{3}\cdot\frac{a\sqrt{3}}{2}\right)^2+b^2=H^2$

b)

$\left(\frac{1}{3}\cdot\frac{a\sqrt{3}}{2}\right)^2+H^2=b^2$

c)

$\left(\frac{2}{3}\cdot\frac{a\sqrt{3}}{2}\right)^2+H^2=b^2$

d)

$\left(\frac{2}{3}\cdot\frac{a\sqrt{3}}{2}\right)^2+b^2=H^2$

16.

For this regular pyramid it is true that:

a)

$a^2+b^2=h^2$

b)

$a^2+H^2=b^2$

c)

$\left(\frac{2}{3}\cdot\frac{a\sqrt{3}}{2}\right)^2+H^2=h^2$

d)

$\left(\frac{1}{3}\cdot\frac{a\sqrt{3}}{2}\right)^2+H^2=h^2$

17.

The area of the cross-section you can see in the picture equals:

a)

$\frac{1}{2}\cdot2a\cdot H$

b)

$\frac{1}{2}\cdot2a\cdot h$

c)

$\frac{1}{2}\cdot a\cdot H$

d)

$\frac{1}{2}\cdot a\cdot h$

18.

For this regular pyramid it ist true that:

a)

$\left(\frac{a\sqrt{3}}{2}\right)^2+H^2=b^2$

b)

$a^2+H^2=b^2$

c)

$\left(a\sqrt{2}\right)^2+H^2=b^2$

d)

$\left(a\sqrt{3}\right)^2+H^2=b^2$

19.

For this regular pyramid it is true that:

a)

$\left(a\sqrt{3}\right)^2+h^2=H^2$

b)

$\left(\frac{a\sqrt{3}}{2}\right)^2+h^2=H^2$

c)

$\left(\frac{a\sqrt{3}}{2}\right)^2+H^2=h^2$

d)

$\left(a\sqrt{3}\right)^2+H^2=h^2$

20.

The lateral edge in this regular pyramid equals:

a)

$\frac{a\sqrt{3}}{2}$

b)

$a$

c)

$a\sqrt{3}$

d)

$a\sqrt{2}$

Equations Pyramid

Total questions: 20

Worksheet time: 10mins

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