Question

A solid oblique pyramid has a square base with an edge length of 2 cm. Angle bac measures 45°. A solid oblique pyramid has a square base with an edge length of 2 centimeters. Point b is the apex and point a is the center of the square base. Line b c is the height of the pyramid. Triangle b c a is a right triangle. Base a c has a length of 3. 6 centimeters. What is the volume of the pyramid? 2. 4 cm3 3. 6 cm3 4. 8 cm3 7. 2 cm3.

Answer 1

Volume of the pyramid with square base which has edge length 2 cm and measure of an angle BAC is 45° is equal to 4.8cm³.

As given in the question,

Edge length of a pyramid = 2cm

Base is square

Base area = (2)²

In right triangle BCA

A is the center of the square base

B is the apex

m ∠BAC = 45°

⇒ m ∠ABC = 45°

⇒AC = BC

Length of AC = 3.6cm

⇒BC = 3.6cm (height)

Volume of the pyramid = (1/3) base area × height

                                    = (1/3) × (2)² × 3.6

                                    = 4.8cm³

Therefore, volume of the pyramid with square base which has edge length 2 cm and measure of an angle BAC is 45° is equal to 4.8cm³.

The complete question is :

A solid oblique pyramid has a square base with an edge length of 2 cm. Angle bac measures 45°.

Point B is the apex and point A is the center of the square base. Line BC is the height of the pyramid. Triangle BCA is a right triangle. Base AC has a length of 3. 6 centimeters. What is the volume of the pyramid?

a. 2. 4 cm³      b. 3. 6 cm³      c.  4. 8 cm³          d. 7. 2 cm³.

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