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Pavlova-9 [17]
1 year ago
10

What is the value of a?

Mathematics
1 answer:
Anna007 [38]1 year ago
5 0

Answer:

15 units

Step-by-step explanation:

By using the Pythagoras Theorem,

C^2 = A^2 + B^2

Substitute in the given values,

25^2 = a^2 + 20^2

625 = a^2 + 400

625 - 400 = a^2 + 400 - 400

a^2 = 225

a =  \sqrt{225}

= 15

Hope this too helped! ^^

I'd recommend watching a video or two on the topic of Pythagoras Theorem, if this explanation isn't clear enough.

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All of the edges of a regular triangular pyramid have length 12. A frustum of the pyramid has height half of that of the pyramid
vlada-n [284]

Answer:

1) The volume of the frustum is 27·(√3)·h

2) The surface area the frustum is 24·h + 54·√3

Step-by-step explanation:

1) A frustum of the regular triangular prism is a portion of the triangular prism

The length of the edge of the triangle prism = 12

The area of the triangular face, A = (√3/4)·a²

∴ A = (√3/4)·12² = 36·√3

When

The volume of the triangular prism, V = A·h = (36·√3)·h

By triangle proportionality theorem, the cross sectional area of the top half of the triangular prism =  (√3/4)·6² = 9·(√3)

The volume of the top half, V₂ = 9·(√3)·h

The volume of the frustum = V - V₂ = (36·√3)·h - 9·(√3)·h = 27·(√3)·h

The volume of the frustum = 27·(√3)·h

2) The surface area of the triangular side of the frustum is given as follows;

A = 36·√3- 9·(√3) = 27·(√3)

The surface area the frustum, F_A = 2×27·(√3) + 2 ×6 ×h + 12×h = 24·h + 54·√3

The surface area the frustum = 24·h + 54·√3

4 0
3 years ago
Find the smallest value of k such that 3240k is a perfect cube
Zarrin [17]

Answer:

225

Step-by-step explanation:

3240k = 2×2×2×3×3×3×3×5×k

Every factor should be in groups of 3

(3×5)² = k

k = 225

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Answer:

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