Question

The base of a right pyramid with apex V is the square ABCD of side 10cm. The length of each slant edge is 15cm. Calculate the;
a.) height of the pyramid
b.)total surface area of the pyramid
c.) volume of the pyramid

Answer 1

Answer:

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Answer 2

Answer:

a) Height of pyramid = 5√5 cm.

b) Total surface area = 400 cm²

c) Volume of pyramid = 500√5 / 3 cm³.

Step-by-step explanation:

Given :- Length of base = 10 cm.

             Length of slant edge = 15 cm.

To Find :- Height of pyramid, Total surface area of the pyramid, Volume of pyramid

Solution :-

Length of base = 10 cm.

Length of slant edge = 15 cm.

We know that,

                        hypotnuse² = base² + height²

Putting given values in the above formula, we get

⇒ 15² = 10² + height²

⇒ height² = 225 - 100

⇒ height = √125

⇒ height = 5√5 cm.

Since base is a square.

∴ Perimeter = 4a = 4 × 10 = 40 cm.

We know that,

        Total surface area = Lateral surface area + base of pyramid

                                      = 1/2 × perimeter × slant height + length × width

∴ Total surface area = 1/2 × 40 × 15 + 10 × 10

                                  = 20 × 15 + 100

                                  = 300 + 100

                                  = 400 cm²

We know that,

                    Volume of pyramid = 1/3 × base × height of pyramid

                                                     = 1/3 × (10 × 10) × 5√5

                                                     = ( 500√5 )/3

Therefore, a) Height of pyramid = 5√5 cm.

                  b) Total surface area = 400 cm²

                  c) Volume of pyramid = 500√5 / 3 cm³.

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