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Worksheet: Applications of Similarity of Solids

Q1:

Given that these two triangular prisms are similar, find the value of π‘₯ .

Q2:

Given that these two triangular prisms are similar, find the value of π‘₯ .

Q3:

If the pair of triangular prisms are similar, and the surface area of the smaller one is 198 yd2, find the surface area of the larger one.

Q4:

A pair of square pyramids are similar. Pyramid A has a base side of 125 in. and a slant height of 160 in, and pyramid B has a base side of π‘₯ in. and a slant height of 32 in. Determine the value of π‘₯ .

Q5:

A pair of square pyramids are similar. Pyramid A has a base side of 25 in. and a slant height of 175 in, and pyramid B has a base side of π‘₯ in. and a slant height of 35 in. Determine the value of π‘₯ .

Q6:

A pair of square pyramids are similar. Pyramid A has a base side of 70 in. and a slant height of 100 in, and pyramid B has a base side of π‘₯ in. and a slant height of 20 in. Determine the value of π‘₯ .

Q7:

A pair of rectangular prisms are similar. Prism 𝐴 is 104 by 32 by 24 inches, while prism 𝐡 is 26 by 8 by π‘₯ inches. Find π‘₯ .

Q8:

A pair of regular triangular pyramids are similar. Pyramid A has a base side of 17 inches and a slant height of 20 inches, whereas pyramid B has a base side of π‘₯ inches and a slant height of 42 inches. Determine the value of π‘₯ .

Q9:

The figure shows two cubes. If the area of the smaller one is 143, and the sides are in the ratio 1 ∢ 5 , what is the surface area of the larger cube?

Q10:

A pair of cylinders are similar. Cylinder A has a base radius of 29 inches and a length of 6 inches, and cylinder B has a base radius of π‘₯ inches and a length of 18 inches. Determine the value of π‘₯ .

Q11:

A cone has a volume of 11 756 cubic centimeters. Suppose that its dimensions were reduced to the current value, find the volume of the resulting cone.

Q12:

The surface areas of two similar solids are 64 square yards and 361 square yards. Find the ratio of their linear measures.

  • A 6 4 3 6 1
  • B 6 4 4 2 5
  • C 1 9 2 7
  • D 8 1 9
  • E 8 2 7

Q13:

A pair of cones are similar. Cone A has a base radius of 17 cm and a slant height of 20 cm, whereas cone B has a base radius of π‘₯ cm and a slant height of 48 cm. Determine the value of π‘₯ .

Q14:

The given pair of rectangular prisms are similar. If the surface area of the smaller rectangular prism is 310 yd2, determine the surface area of the larger one.